A modeling using the maximum growth capacity of Hantzschia amphioxys in the Homa Lagoon

Homa lagoon found in the Izmir bay, Aegean Sea, is important because it is the last lagoon in which fishing activities are carried out. Hantzschia amphioxys species, on which this study was carried on, are benthic diatoms and they are isolated from Homa Lagoon. The Monod equation expressing the nutrient dependency of the growth rates can also be used for carrying capacity (with different parameter values; chl-a max, Ks). Temporal changes of the calculated maximum chl-a concentrations (carrying capacity) was 115 μg chl-a/L by determining the hyperbolical relations between the maximum biomass levels (biomass carrying capacity) and nutrient concentrations obtained from the phytoplankton growth graphs.


INTRODUCTION
Fossil records of diatoms were found about 185 years ago (Rothpletz, 1896;Gersonde and Harwood, 1990).Diatoms are found in a wide variety of habitats including ice and soil, and they are also commonly found in both seas and freshwaters (Werner, 1977).Diatoms are the main components of phytoplankton organisms for many aquatic ecosystems.
They are named microphytobenthos in coastal areas.Moreover, they are found in high rates in the tide zones of many bays.Benthic diatoms contribute to 50% of total primary production (Perrissinotto et al., 2000;Montani et al., 2003).It is reported that diatoms have an important role in global biogeochemical cycle of nitrogen and carbon (Serodio, 2003).Furthermore, coastal waters are characterized by abundance of diatoms (Nelson et al., 1995).
In coastal waters, wave, wind, entrance of freshwater, etc. processes cause short term variations in hydro-dynamic and chemical conditions of upper water column.In the subsequent process, increase of primary production is observed (Fouilland et al., 2007).Production of microphytobenthos has hourly, weekly, monthly, and seasonally changing characteristics in the tide zones of bays (Shaffer and Onuf, 1985;Pinckney and Zingmark, 1991;Smith and Underwood, 1998;Serodio and Catarino, 2000).
Lagoon fields cause strong water and tide movements cause the rich water found at the bottom to flow out or cause the poor water found outside to flow in.Since water is shallow at these regions, the nutrients originating from the regeneration at the bottom are used more by benthic algae (Kutlu, 2000).Diatoms are the main components of the phytoplanktons which also serve as an important nutrient source for all aquaculture (St. John et al., 2001).Therefore, they are very important for lagoon fields.*Corresponding author.E-mail: banukutlu@tunceli.edu.tr or kutlubanu@gmail.com.Tel: +90.94282131784.
Although, the number of the kinetic studies for the Hantzschia genus, which includes the Hantzschia amphioxys species, is very few, the number of studies on the H. amphioxys species, which forms the subject of this study, is scarce.There is no study present about the isolation of the H. amphioxys species and determination of the kinetic parameters on its discontinuous mono culture.
The purpose of this study was to research the maximum growth capacity and the carrying capacity of the H. amphioxys species in the medium with nutrient limited discontinuous culture system and optimum temperature.

MATERIALS AND METHODS
H. amphioxys was isolated from the surface sea water of the Homa Lagoon, which was filtered before f/2 was added and replicate cultures were maintained, from Izmir Bay (Aegean Sea) by using the dilution method under conditions presenting with a 11 ± 0.5°C temperature, ‰ 33 salinity, 24 L: 0D day length, 52 μmol photon.m 2 s-1 light intensity; 40 W day light fluorescent and f/2 enrichment medium.Turner Design 10AU field fluorometre was equipped with in vivo Chl-a filter set and calibrated with the culture of H. amphioxys using Hatch -Lange Model DR4000 spektrophotometer and three coloromatic method (Strickland and Parsons, (1972).
The culture medium prepared was incubated under constant (25, 45, 52, 58 and 65 µmol/m 2 s) light intensities at 6, 12, 15, 16.5, 18, 20 and 25°C temperatures and the exponential phase was monitored.The measurements were estimated as the amount of chl a using the Turner Designs 10-AU Field Floumeter (Guillard, 1975;Guillard and Rather 1962;Brand and Guillard, 1981).The chlorophyll based specific growth rates were calculated following Guillard (1973): Firstly, their growth rates in response to temperature were plotted.Each temperature value in the chart represented the experimental point for five different light intensities.The optimum growth rate was obtained under the conditions of 1.711 day -1 and 18°C and 52 µmol/m 2 s light intensity.This result was defined as µopt.A curve was fitted that matched the experimental points in the chart.In order for this curve to include growth inhibition, the growth rates were obtained.Vollenweider (1965)'s formula describing the photosynthesis/light curves was modified and used to represent temperature curves (µ= µ max*f(T)*h(T) ).h (T)= is a function describing inhibition.The whole Equation is as follows: Maximum Chl-a value in each growth curve (Chl-a/time) was recorded as biomass carrying capacity (BCC).Relationships (like µ/properties, BCC/temperatures, BCC/I, BCC/nutrient concentrations) were investigated statistically.The maximum biomass carrying capacity (BCCmax) and the half-saturation constants were calculated with the help of the Michaelis-Menten Equation.All the half saturation constants for BCC/I curves (for seven different temperatures) were not statistically significant (p = 0.55).But the calculated values of BCC max were statistically significant (p<0.005),expect for 16.5 and 20°C.
The maximum biomass carrying capacity (BCCmax) and the half- Kutlu and Buyukisik 1155 saturation constants were calculated with the help of the Michaelis-Menten Equation.All the half saturation constants for BCC/ I curves (for seven different temperatures) were not statistically significant (p = 0.55) but the calculated values of BCCmax were statistically significant (p<0.005),except for 16.5 and 20.0°C.

Temperature
The research was made on seven different temperature values (6, 12, 15, 16.5, 18, 20 and 25°C) with the purpose of determining the optimal temperature of the H. amphioxys species used in the study.Test temperatures of the research were chosen considering the seasonal properties of the Homa Fishery.Exponential growth phase of the H. amphioxys species was reached quicker than expected at 6°C in discontinuous culture system.At 12°C in the discontinuous culture system of the H. amphioxys species, it was observed that the species did not enter the lag phase and they went into the exponential growth phase.When the temperature was raised to 18°C, the H. amphioxys species was observed to enter the lag phase in the 1 st day and in the following days it was observed to enter the exponential growth phase.
When the temperature was raised to 20°C, the cells of the H. amphioxys species were observed to enter the lag phase in the 1 st day.When the effects of the discontinuous culture system and nutrient limited conditions on the growth of H. amphioxys are examined at the intensity of light, which is the highest temperature, it was observed that the species enter the growth phase faster than expected like all temperatures.
The carrying capacity of the lagoon water for the H. amphioxys species changed in a polynomial relation with the temperature (Figure 1).When the temperature decreased below 10°C, the maximum chl-a value obtained rapidly decreased.It was found to be constant between 10 and 20°C, and again an increase was observed between 20 to 25°C.

Nitrate
Potential maximum chl-a values for nitrate were found to be 158.83± 113.7 µg chl-a/L and the half-saturation coefficients (K s ı ) were found to be 190.11 ± 184.7 (Figure 2).According to the results of the statistical analysis made by the least squares method, the variation in the nitrate concentration gives the carrying capacity of water to be 98%.
For the H. amphioxys species, in adequately high concentrations, nitrate substantially increased the carrying capacity of water with regards to reactive phosphate (Table 1 and Figure 2

Reactive phosphate
Potential maximum chl-a values for reactive phosphate were found to be 15.90 ± 2.73 µg chl-a/L and the halfsaturation coefficients (K s ı ) was found to be 1.798 ± 0.974.According to the results of the statistical analysis made by the least squares method, the variation in the phosphate concentration gives the carrying capacity of water as 90% (Figure 3).
Temporal changes of the calculated maximum chlconcentrations (carrying capacity) are given in Figure 4.In Figure 4, the curve found in the upper part shows the effect of temperature on the carrying capacity, and the carrying capacity of lagoon water for the species in question reaches the maximum value of 115 µg chl-a/L from June to the end of September.However, the observed values (in situ) were substantially low (Figure 4).Moreover, the in situ chl-a concentrations denote the biomass of the community.Biomass of the H. amphioxys species is less in this total biomass.The Monod equation expressing the nutrient dependency of the growth rates can also be used for carrying capacity (with different parameter values; chl-a max, K s ı ).Nutrients substantially decrease the carrying capacity of lagoon water all year around and while the nitrogenous compounds are the carrying capacity limiting nutrients, they are also found to be limiting the growth rate (Table 1).
Medium concentrations of nutrients decrease the carrying capacity of the lagoon water for the H. amphioxys species below 5 µg/L (<5 µg/L).In situ chl-a values are smaller than the carrying capacity that is limited by the nutrients.This is due to the contributions of the possible loss terms, which are advective transportation and grazing, because they are statistically calculated from the values obtained from the carrying capacity.Therefore, they do not include grazing and advective transportation components.

DISCUSSION
The fact that lagoons are shallow and deep, water mixes with water column results in the nutrients' turning back into the medium very fast.The rich deep water's rapidly transferred to the surface means a significant increase in the amount of production.The temporal variations of the growth rate and the maximum chl-concentrations that the species can reach were calculated, considering the temporal variations of the temperature and nutrient concentrations in the lagoon.With the water temperature decreasing to 7°C in February and December, substantial negative effects of water temperature was found.Limiting effects of nutrients have been clearly observed.Small increases were observed in growth rates in March, July, September and October.Growth rates substantially decreased in other months.In response to temperature and more significant nutrient concentrations, the carrying capacity of the lagoon water increased in March, July,

Kutlu and Buyukisik 1157
Table 1.Temporal changes of the calculated maximum chl-a concentrations (carrying capacity).

Month
In  September, October and November.However, in March and July, while the in situ chl-a values were observed to be lower than the values determined from the model, small increases was observed.
Reproduction of the H. amphioxys species all the year around in the lagoon is limited by in situ nutrient concentrations and by the temperature in very cold months of winter.They can be observed in the lagoon in March, July and September.The period we found shows analogy with the study made by Sabanci (2008).Nutrient limited growth for this species has been reactive limited phosphate in February, while it was limited by nitrogenous compounds in the other months.Due to the lipid synthesis observed in silicate limited growth, the surface layer of the sediment will be rich in lipids.This situation shows that, they can have a great role in nutrition of sea bream seed fish, which is a demersal fish and gastropods (Xing et al., 2008) with bottom mud.
A detailed research has not been made yet on the benthic diatoms, which have a great role in nutrition of crustaceans (Pena de la, 2007) and gastropods (Xing et al., 2008).With this study, by revealing the growth kinetics of the benthic diatoms, contribution will be made to dynamic applications related to nutrition of crustaceans and fish.
With this study, including application of the carrying capacity to the Homa Lagoon, it can be concluded that the carrying capacity can be also applied to fish breeding farms (fisheries).At the same time, in demersal fish farming, lipid production of the H. amphioxys species at the bottom would have positive contributions on the species nourished in net cages, which also cover the bottom.
By uptake of mineralization products in the sediment by these species, eutrophication will be prevented to some extent (by keeping the produced nutrients in the sediment by algae).Our goal was to determine the growth rate of all nutrients and the maximum levels of the phytoplankton biomass (the maximum biomass carrying capacity) in the case of how full growth can be reached and at what level the nutrient restrictive growth keeps the biomass (biomass carrying capacity) and the nutrient(s) that sustain year long growth.By determining the hyperbolical relations between the maximum biomass levels (biomass carrying capacity) and nutrient concentrations obtained from phytoplankton growth graphs, we tried to apply flexible models which will restrict the levels phytoplankton can reach.
Concentrating on the well-known importance of N as a limiting nutrient (Carthy and Carpenter, 1983;Dugdale and Goering, 1967), those models tracked the supply of nitrate (NO 3 -) via upwelling and mixing, its uptake by phytoplankton and biological regeneration of N as ammonium (NH 4 + ) in surface waters.Other modeling efforts, beginning with the pioneering work of Walsh (1975) have explicitly considered growth limitation by light, and by two or more nutrients.They have simulated the cycling of up to four elements (C, N, P and Si) in surface waters, and allowed for the depletion of up to four nutrients (NO 3 , NH 4 + , PO 4 and Si(OH) 4 ) to limiting concentrations.Almost all, recent multielement models (Dugdale and Wilkerson, 1998;Pondaven et al., 1998;Spitz et al.,2001) have included two or more phytoplankton groups with qualitatively different nutrient requirements, such as diatoms (which take up Si(OH) 4 and require Si for growth) and non-siliceous picoplankton (which do not take up Si(OH) 4 ).This study experimented four different nutrient groups and nutrient requirements of H. amphioxys were determined, and a simple model was comprised of nutrient requirements of phytoplankton in the Homa Lagoon.Mongin et al. (2003) showed that this has the effect of causing chlorophyll a to be limited by cellular N when N limits phytoplankton growth (for example, in surface waters in summer) and by cellular C when light limits growth (for example, within the DCM).In our study, it was found that the H. amphioxys species in the community in the Homa Lagoon was N restrictive for all the study period except two months.

Figure 1 .
Figure 1.Relationship of potential carrying capacity (in light and nutrient saturation) versus temperature.

Figure 4 .
Figure 4. Temporal changes of the calculated maximum chl-a (carrying capacity).