Directory UMM :Data Elmu:jurnal:J-a:Journal of Experimental Marine Biology and Ecology:Vol241.Issue2.Aug1999:

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Journal of Experimental Marine Biology and Ecology, 241 (1999) 285–299

Interactions between the red tide dinoflagellates Heterocapsa

circularisquama and Gymnodinium mikimotoi in laboratory

culture

a ,_* b a a

Takuji Uchida , Satoru Toda , Yukihiko Matsuyama , Mineo Yamaguchi ,

a c

Yuichi Kotani , Tsuneo Honjo

National Research Institute of Fisheries and Environment of Inland Sea, Maruishi, Ohno, Saiki,

Hiroshima739-0452, Japan

National Research Institute of Aquaculture, Nansei, Watarai, Mie 516-0193, Japan

Faculty of Agriculture, Kyushu University, Hakozaki, Higasiku, Fukuoka 812-0053, Japan Received 6 November 1998; received in revised form 21 May 1999; accepted 23 June 1999

Abstract

Interactions between Heterocapsa circularisquama and Gymnodinium mikimotoi, causative red tide dinoflagellates, were investigated using bialgal cultures. G. mikimotoi was killed by H.

circularisquama when the initial cell density of each species was set at 200 cells ml . However, cells of H. circularisquama transformed to temporary cysts when the initial cell density of G.

mikimotoi was increased to 2000 cells ml . Thus the interaction between H. circularisquama and

G. mikimotoi was found to be dependent upon the initial cell densities of the two species. Culture filtrate of H. circularisquama induced no inhibitory effect on the growth of G. mikimotoi. Similarly when separated by a membrane filter, G. mikimotoi grew well when cultured with H.

circularisquama. G. mikimotoi appear to be killed by cell contact with H. circularisquama. In growth experiments using a culture filtrate of G. mikimotoi and cultures separated by a membrane filter, G. mikimotoi was shown to secrete a substance that inhibited the growth of H.

circularisquama. However, the inhibitory effect of the medium was found at higher cell densities

of G. mikimotoi than in the bialgal cultures at which the growth of H. circularisquama was suppressed and formed temporary cysts. It is likely that the inhibitory effect of G. mikimotoi on H.

circularisquama in the bialgal cultures occurred mainly by direct cell contact. The growth of H.

circularisquama and G. mikimotoi in the bialgal cultures was simulated using a mathematical model to quantify the interaction. The degree that G. mikimotoi was inhibited by H.

circularis-quama was found to be three times larger than the inhibitory effect of G. mikimotoi on H.

*Corresponding author. Tel.:181-829-550-666; fax:181-829-541-216.

E-mail address: [email protected] (T. Uchida)

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Keywords: Cell contact; Gymnodinium mikimotoi; Heterocapsa circularisquama; Red tide; Species inter-action; Temporary cyst

1. Introduction

Heterocapsa circularisquama Horiguchi is a novel red tide causing species of which occurrences have been increasing in embayments of west Japan. This species has caused significant damage to shellfish aquaculture by killing the bivalves (Matsuyama et al., 1995; Nagai et al., 1996). Several physiological and ecological studies have been conducted in order to clarify the mechanism of red tide outbreaks of this species (Uchida et al., 1995; Yamaguchi et al., 1997; Matsuyama et al., 1995, 1996). Matsuyama et al. (1996) showed that the disturbance of water stratification is a likely mechanism triggering the red tide occurrences of H. circularisquama. Yamaguchi et al. (1997) reported that this species prefers higher temperatures compared to other representative red tide species of Japan. In addition to physical and chemical factors, species interactions are also considered to be important for the development of phytoplankton blooms. H. circularisquama sometimes appears after the bloom of Gymnodinium mikimotoi Miyake et Kominami ex Oda which is one of the most representative red tide flagellate in Japan. For example, red tide by H. circularisquama replaced G. mikimotoi red tide at Gokasho Bay in August 1994 (Uchida, unpublished data). The same sequence pattern from G. mikimotoi to H. circularisquama was observed at Hiroshima Bay in August 1998 (Matsuyama, unpublished data). It is possible that H. circularisquama and G. mikimotoi interact with each other in nature.

Growth interactions between phytoplankton species mediated by extracellular organic substances released (allelopathy) by one or both interacting species have been consid-ered an important factor affecting phytoplankton sequence (Maestrini and Bonin, 1981; Rice, 1984; Honjo, 1994). For example, Pratt (1966) observed the alternate appearances of Olisthodiscus luteus and Skeletonema costatum, and verified that O. luteus produces a substance inhibiting the growth of S. costatum. Similarly, some flagellate species have been found to secrete substance inhibiting coexisting phytoplankton species (Uchida, 1977; Honjo et al., 1978).

Differing from ‘allelopathy’, Uchida et al. (1995) found that H. circularisquama is able to kill the dinoflagellate Gyrodinium instriatum by direct cell contact. Furthermore, several species of flagellates have been observed to die when cultured with H. circularisquama (Uchida et al., 1996), although it was not clear if cell contact caused this phenomenon. On the other hand, H. circularisquama has been shown to be suppressed in bialgal cultures by several diatom species (Uchida et al., 1996). In this case, H. circularisquama is transformed into immotile cells with a round or elliptical form. Thus, unique interactions have been observed between H. circularisquama and other phytoplankton species.

Subsequently, we have extended these investigations to examine the relationships between H. circularisquama and Gymnodinium mikimotoi. This study deals with the effect of initial cell density on the competitive success between these two dinoflagellates.

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Furthermore, the growth of each species in bialgal cultures were simulated using a mathematical model to quantify the relationships between H. circularisquama and G. mikimotoi.

2. Materials and methods

The strains of Heterocapsa circularisquama (HA 92-1) and Gymnodinium mikimotoi (GM-1) used were isolated from seawater samples collected from Ago Bay, Japan in December 1992, and from Hiroshima Bay, Japan in July 1992, respectively. Clonal cultures of these species were obtained by repeated washings using capillary pipettes.

The cultures thus obtained were subjected to sterility tests using ST10 medium (Ishida et al., 1986). In both cultures, bacterial growth was not observed. Cultures were maintained at 22618C on a 12-h light / dark cycle; illumination was provided by

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cool-white fluorescent lamps at 90–120 mmol photon m s . Modified SWM3 (Itoh and Imai, 1987) was used as the culture medium throughout the experiments. Growth experiments using bialgal cultures were conducted in 50-ml Erlenmyer flasks with 25 ml of medium. Cells of H. circularisquama in the logarithmic phase of growth were

inoculated at a density of 200 cells ml into cultures of G. mikimotoi of three different

cell densities: 200, 1000 and 2000 cells ml . Growth was measured at 2–5 day intervals by counting cells in 0.01–0.2-ml culture samples using a Sedgwick–Rafter

slide. When cell densities were greater than 20 000 cells ml , the samples were diluted 10–20 times with autoclaved seawater. The condition of the algal cells in the bialgal cultures were observed using an inverted microscope.

Culture filtrates of H. circularisquama and G. mikimotoi were tested in order to verify the effects of extracellular products on the growth of the other species. Cultures of each

species of which the cell density reached 23 000 cells ml for H. circularisquama, and

4600 and 44 000 cells ml for G. mikimotoi, were passed through membrane filters (Millipore RA, pore size 1.2 mm). Then the pH of the filtrate was adjusted to 7.8–8.0 with 1 N HCl. When necessary, it was re-enriched with nutrients at the same concentrations of the modified SWM3. The filtrates thus prepared were sterilized by passing through a membrane filter (Kurabou Steradisc 25, pore size 0.2 mm). Growth experiments were conducted using glassware test tubes with 4.5 ml of the filtrate or modified SWM3. Culture conditions were the same as stated above. Growth was measured by in vivo chlorophyll a fluorescence using a Turner Designs Model 10-100R fluorometer (Brand et al., 1981).

H. circularisquama and G. mikimotoi were also cultured being separated from each other with a membrane filter. Half-milliliter cultures of both species were put in each well of 24-well multiplates. The initial cell density of the cultures were 30 000 cells

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ml for H. circularisquama, and 4300 cells ml , 9700 cells ml , and 29 000 cells

ml for G. mikimotoi. As a control, the flagellate culture was replaced with fresh modified SWM3 medium. Then, a small chamber (Millicell PC) with a membrane filter (pore size 3 mm) fixed to its base containing 0.5 ml of the other species culture was

placed into each well. The cell density in this small chamber was 200 cells ml for both species. Thus we tested if the species outside of the chamber released any inhibitory

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substance on the other species cultured in the chamber. These procedures were conducted aseptically throughout the experiments. These cultures were carried out under the same conditions as the bialgal cultures detailed above. After each set of the cultures, cell morphology was carefully observed each day under an inverted microscope. Then cell density was determined by counting cells in 0.01–0.1-ml culture samples 4 days after the inoculation.

3. Results

3.1. Bialgal cultures

Results of the bialgal cultures are shown in Fig. 1. When H. circularisquama and G.

mikimotoi were inoculated at densities of 200 cells ml , the growth of H. circularis-quama in bialgal cultures was almost the same as in the monoalgal cultures (control) (Fig. 1A). However, the growth of G. mikimotoi was dramatically suppressed within 2 days after inoculation in the bialgal cultures with H. circularisquama, although in monoalgal culture G. mikimotoi showed exponential growth to the end of the experi-ment. G. mikimotoi cells had completely died 4 days after inoculation in the bialgal culture. In this case, the cells became round and finally burst.

Fig. 1B shows the growth of each species in bialgal and monoalgal cultures when the

initial cell density of G. mikimotoi was 1000 cells ml , and H. circularisquamama at

200 cells ml . The results show almost the same tendency as initial cell densities of

200 cells ml . The growth of G. mikimotoi was extremely depressed, however, the decrease of cell density was relatively moderate in this case.

21 When the initial cell density of G. mikimotoi was increased to 2000 cells ml , the growth profile of both species entirely changed. The growth of H. circularisquama was suppressed, and G. mikimotoi showed active growth compared to the former two cases (Fig. 1C). Furthermore, cells of H. circularisqua became immotile and round to spherical in shape as observed in bialgal cultures with some diatom species (Uchida et al., 1996). These immotile cells of H. circularisqua recovered to the motile form again when isolated and cultured in fresh medium. Some of these immotile cells became motile within 24 h after isolation in fresh medium.

3.2. Growth in culture filtrates

Fig. 2 shows the growth of G. mikimotoi in the filtrate of H. circularisquama culture. G. mikimotoi grew as well as the control although the culture filtrate had not been enriched.

H. circularisquama in the culture filtrate of G. mikimotoi, prepared from a G.

mikimotoi culture of 4600 cells ml , grew as well as the control during the first 6 days from the inoculation although the final growth was slightly depressed compared to the control (Fig. 3A). However, the filtrate of G. mikimotoi culture with a density of 44 000

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Fig. 1. Growth of Heterocapsa circularisquama and Gymnodinium mikimotoi when cultured alone (h, H.

circularisquama;s, G. mikimotoi) and together (j, H. circularisquama;d, G. mikimotoi) varying the initial cell density of G. mikimotoi in each experiment. Initial cell density of G. mikimotoi was adjusted to 200 (A),

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1000 (B), and 2000 cells ml (C), while that of H. circularisquama was constant at 200 cells ml in each experiment. Vertical lines show the standard deviation of the mean (n53). When cell densities were lower than

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Fig. 2. Growth of Gymnodinium mikimotoi in culture filtrate of Heterocapsa circularisquama. H. circularis-21

quama culture of 23 800 cells ml was used for the preparation of the filtrate (s, control (modified SWM3);

d, culture filtrate of H. circularisquama). Vertical lines show the standard deviation (n53).

3B). The final cell density reached was only about 10 of the control. Most of the H. circularisquama cells were in a motile form, and immotile round-elliptical cells were less than 40% of the total cells.

3.3. Growth in culture when separated with a membrane filter

Fig. 4 shows the growth of G. mikimotoi when cultured with a high cell density of H.

circularisquama (initial cell density530 000 cells ml ) separated by a membrane filter. The growth of G. mikimotoi 4 days after the start of the experiment does not significantly differ from the control ( p.0.2). That is, growth inhibition of G. mikimotoi by H. circularisquama was not observed.

Fig. 5 shows the growth of H. circularisquama cultured with G. mikimotoi at various

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Fig. 3. Growth of Heterocapsa circularisquama in culture filtrate of Gymnodinium mikimotoi. G. mikimotoi

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culture of a cell density of 4600 cells ml was used in A, and that of 44 000 cells ml in B, respectively (h, control (modified SWM3); j, culture filtrate of Gymnodinium mikimotoi; m, enriched culture filtrate of

Gymnodinium mikimotoi ). Vertical lines show the standard deviation (n53).

The growth of H. circularisquama with G. mikimotoi at an initial cell density of 4300

and 9700 cells ml was not significantly different from that of the control ( p.0.2 and .0.05, respectively). On the other hand, the growth of H. circularisquama was suppressed significantly ( p,0.05) when the initial cell density of G. mikimotoi was

29 000 cells ml . In this case, however, most cells of H. circularisquama showed active motility, and did not form immotile round cells as observed in bialgal cultures.

4. Discussion

4.1. Interaction between H. circularisquama and G. mikimotoi

It is clear that H. circularisquama and G. mikimotoi interfere with each other. When

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the initial cell density was 200 or 1000 cells ml for G. mikimotoi and 200 cells ml for H. circularisquama in the bialgal cultures, G. mikimotoi was found to be inhibited and finally died. Uchida et al. (1995, 1996) reported that H. circularisquama kills some other flagellate species when cultured together. The ability of H. circularisquama to kill other flagellates may contribute to keeping itself dominant in a flagellate community. In the present study, the growth of G. mikimotoi seems to be suppressed by cell contact

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Fig. 4. Cell density of Gymnodinium mikimotoi 4 days after inoculation when cultured separated from

Heterocapsa circularisquama with a membrane filter. G. mikimotoi was cultured in a chamber with a membrane filter over the base, and H. circularisquama was cultured outside the chamber. G. mikimotoi was

inoculated at a cell density of 200 cells ml . The initial cell density of H. circularisquama outside the

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chamber was adjusted to 30 000 cells ml , of which the culture finally reached 272 000 cells ml in the mean (n53, S.D.: 39 914) at the end of the experiments. Vertical lines indicate the standard deviation (n53). with H. circularisquama as also observed between H. circularisquama and Gyrodinium instriatum (Uchida et al., 1995). However, since the culture filtrate of H. circularis-quama at a high cell density did not show any inhibitory effect on G. mikimotoi, and G. mikimotoi grew well when cultured with H. circularisquama separated by a membrane filter, this indicates that a growth inhibiting substance is not secreted by H. circularis-quama, or, if secreted, it is in too small an amount to surpress the growth of G. mikimotoi. In the case of the interaction between G. instriatum and H. circularisquama, G. instriatum cells became immotile immediately after contact with H. circularisquama although in some cases immobilized G. instriatum cells later recovered their motility (Uchida et al., 1995). However, G. mikimotoi did not show any distinct morphological changes after contact with H. circularisquama. It is most likely that G. mikimotoi growth was suppressed and finally death occurred after repeated cell contacts with H. circularisquama.

21 When the initial cell density in the bialgal culture was set at 200 cells ml for H.

circularisquama and at 2000 cells ml for G. mikimotoi, the growth of H. circularis-quama was suppressed with the cells transforming into immotile, round-elliptical cells on the bottom of culture vessels. Thus H. circularisquama undergoes a morphological change in the presence of a high cell density of G. mikimotoi. These immotile cells of H. circularisquama became motile and grew actively again when isolated in fresh medium. Therefore, they are considered to be temporary cysts as described previously for some other dinoflagellates (Pfiester and Anderson, 1987). The same phenomenon was observed between H. circularisquama and three diatom species (Uchida et al., 1996); cells of H. circularisquama formed temporary cysts when cultured with Chaetoceros

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Fig. 5. Cell density of Heterocapsa circularisquama 4 days after inoculation when cultured separated from

Gymnodinium mikimotoi with a membrane filter. H. circularisquama was cultured in a chamber with a membrane filter over the base, and G. mikimotoi was cultured outside the chamber. H. circularisquama was

inoculated at the cell density of 200 cells ml . The initial cell density of G. mikimotoi outside the chamber 21

was adjusted to 4300, 9700, and 29 000 cells ml , and the final cell density in the mean reached 18 450 21

(n53, S.D.: 1843), 32 200 (n53, S.D.: 3799), 66 000 (n53, S.D.: 7846) cells ml , respectively at the end of the experiments. Vertical lines indicate the standard deviation (n53).

didymus, Stephanopyxis palmeriana and Licmophora sp. The formation of temporary cysts may be regarded as a survival strategy of H. circularisquama to avoid competition with these phytoplankton species although H. circularisquama kills G. mikimotoi when

G. mikimotoi is present at cell densities lower than 1000 cells ml . The culture filtrate

of G. mikimotoi prepared at a final density of 4600 cells ml did not cause an inhibitory effect on the growth of H. circularisquama during the first 6 days from the inoculation, nor cause the formation of temporary cysts of this species. On the other hand, the filtrate

prepared from G. mikimotoi culture at a density of 44 000 cells ml suppressed the growth of H. circularisquama to about 10% of that in the control. The inhibitory effect cannot be attributed to nutrient depletion due to the consumption by G. mikimotoi since re-enrichment of the filtrate did not lead to a recovery of the growth of H. circularis-quama. This shows that G. mikimotoi secretes inhibitory substance into the medium which inhibits H. circularisquama. However, the growth inhibition and temporary cyst formation of H. circularisquama was observed in the early phase of growth at which G.

mikimotoi cell density was less than 5000 cells ml in the bialgal culture. The culture experiments where the two species were separated by a membrane filter showed similar results. The growth of H. circularisquama was almost the same as in the monoalgal culture when G. mikimotoi was inoculated outside the membrane at the cell densities of

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H. circularisquama growth was suppressed to less than half of that in the control and most of the H. circularisquama cells were moving actively. Thus, although G. mikimotoi seems to secrete a substance inhibiting for the growth of H. circularisquama, the inhibitory effect of the medium occurred at higher cell densities of G. mikimotoi than the levels in the bialgal cultures at which the growth of H. circularisquama was suppressed and transformed into temporary cysts. Therefore, it is highly probable that the inhibitory effect of G. mikimotoi on H. circularisquama observed in the bialgal cultures mainly occurred due to cell contact.

If direct cell contact plays an important role in the interaction between phytoplankton assemblages, then this may be beneficial for them compared to the case mediated by a substance released into ambient seawater (allelopathy) from the view of energy efficiency. In the former case, the organism reacts only when it makes contact with another cell. In the latter case, however, the organism need to constantly secrete an interactive substance regardless of the existence of other organisms.

4.2. Growth simulation in bialgal cultures

The growth of H. circularisquama and G. mikimotoi in bialgal cultures was simulated using the following equations:

dx / dt5r x(1x 2x /K )x 2Axy5r x(1x 2(x1ay) /K )x (1) dy / dt5r y(1y 2y /K )y 2Bxy5r y(1y 2(bx1y) /K )y (2)

dz / dt5Axy5(ar /K )x x ?xy (3)

Here, x, y and z are the motile cell densities of H. circularisquama and G. mikimotoi, and immotile H. circularisquama, respectively. Then r and K are the growth rate andx x

carrying capacity of H. circularisquama, and r and K are the corresponding parametersy y

for G. mikimotoi when each species was cultured in a monoalgal culture. A measures the degree of inhibition of H. circularisquama by G. mikimotoi, and B vice versa. When we make A5ar /K , and Bx x 5br /K , Eqs. (1) and (2) become the same formula as for they y

growth of populations competing with each other for limited resources (Iwasa, 1998). Parameters a and b are nondimensional, and measure the degree of inhibition by the other species when compared to the self-interference.

Eqs. (1) and (2) can be approximated with the following equations:

G. mikimotoi, respectively. When each species is cultured in a monoalgal culture, we can put a5b50. The logistic parameters were estimated by Eqs. (4) and (5) using the monoalgal culture data. Then the parameters a and b were calculated using bialgal culture data directly from Eqs. (4) and (5). Moreover, precise estimations of parameters

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a and b were carried out using the following function as a measure of agreement between the observed and estimated growth of x, y and z.

2 2

* *

V(a,b)5

O

hln(x_i 1e)2ln(x )j_i 1

O

hln( y_i 1e)2ln( y )j_i 2

O

hln(zi 1e)2ln(z )ji (6) Here, x , y and z refer to the observed motile cell densities of H. circularisquama andi i i

G. mikimotoi, and immotile H. circularisquama, respectively. The parameters a and b

were changed from 0 to 500. For each set of a and b, the theoretical cell densities, x ,i

* *

yi and zi were calculated by integrating the differential Eqs. (1)–(3) using the Runge–Kutta method, and then the values of V(a,b) were calculated. Since the theoretical cell density may become very small or negative due to calculation error, the

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constante(510 ) was introduced into Eq. (6). The most appropriate values of a and b were determined when V(a,b) became minimum.

The carrying capacity for H. circularisquama (K ) and for G. mikimotoi (K ) wasx y

calculated 352 416 and 92 286 cells ml , respectively (Table 1). The growth rate was

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estimated at 1.039 div. day for H. circularisquama, and 0.485 div. day for G. mikimotoi which were calculated by the conversion from natural logarithms to logarithms of base 2 since both species grow by binary fission (Table 1). The optimum values of a and b were 144 and 245, respectively, as indicated in Table 1. The growth patterns of H. circularisquama and G. mikimotoi calculated using these values of a and b are given in Fig. 6. These growth curves are in good agreement with those obtained in the culture experiments.

Fig. 7 shows the isoclines for which dx / dt50 and dy / dt50, and the trajectories of the population of the two species under the various initial cell densities, which were calculated using the values of parameters given in Table 1. The equilibrium point is at x5392 and y52.514. The estimated parameters show that this is the unstable equilibrium point because Kx,aK and bKy x.K (Iwasa, 1998). Consequently, in anyy

combination of initial densities of the two species, one outcompetes the other and the growth of the other species is suppressed, indicating that the initial cell densities of the species are critical in determining the outcome.

The degree of inhibition on H. circularisquama by G. mikimotoi was calculated at

29 21 21

3.4310 ml cells s (parameter A) and on G. mikimotoi by H. circularisquama at

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11310 ml cells s (parameter B ), respectively (Table 1). Cell contact frequency to cause the death of G. mikimotoi and temporary cyst formation of H. circularisquama

Table 1

Estimated parameters

Carrying Growth rate (r) Interaction rate capacity (K )

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(cells ml ) (h ) (divisions a or b A or B

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day ) (ml cell s )

Heterocapsa circularisquama 352 416 0.030 1.039 144 3.4310

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Fig. 6. Growth simulation of Heterocapsa circularisquama and Gymnodinium mikimotoi in bialgal cultures in which the initial cell density of G. mikimotoi was varied. The initial cell density of G. mikimotoi was: (A) 200,

(B) 1000, and (C) 2000 cells ml . Lines – show the simulated growth curves. G. mikimotoi, motile cells of H. circularisquama, immotile cells of H. circularisquama. The symbols (h_,m_,_^_{) indicate the}

growth of each species observed in bialgal cultures, (h) G. mikimotoi, (m) motile cells of H. circularisquama, (^) immotile cells of H. circularisquama.

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Fig. 7. Isoclines for which dx / dt50 and dy / dt50, and the trajectories of Heterocapsa circularisquama and

Gymnodinium mikimotoi under various initial cell densities. Areas (I)–(IV) are divided by the two lines of

dx / dt50 and dy / dt50. Area I: cell densities of both H. circularisquama and G. mikimotoi decrease; area II: cell density of H. circularisquama increases but that of G. mikimotoi decreases; area III: cell densities of both

H. circularisquama and G. mikimotoi increase; area IV: cell density of H. circularisquama decreases but that of G. mikimotoi increases.

was calculated by comparing these values of parameters A and B and the theoretical cell contact frequency between the two species, assuming that the inhibitory operation between H. circularisquama and G. mikimotoi was realized only by cell contact. If the cells of the two species are assumed to be spherical in shape with the same size and to swim randomly at the same mean speed, the theoretical cell contact frequency can be estimated by an analogy of the molecular kinetic theory.

1 / 2 2

F52 pcd xy (7)

Here, F is the cell contact frequency, c is the mean swimming velocity of the cells, d is the diameter of the cells, and x and y are the cell densities of the two species. The mean cell length, width and height of H. circularisquama are 21.5, 15.3 and 13mm (geometric mean, 16.2mm), and those of G. mikimotoi are 30.4, 28.1 and 8mm (geometric mean, 18.9 mm), respectively. The swimming speed, calculated by measuring the time during

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which a cell passed through a certain distance measured by a micrometer under an

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inverted microscope, is 0.58 m h for H. circularisquama and 0.49 m h for G. mikimotoi. If it is assumed that the cell diameter is 18mm and the swimming velocity is

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0.5 m h for both species, theoretical cell contact frequency is calculated as 2310 xy

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(cell ml s ). By comparing this value with parameters A and B, it is estimated that H. circularisquama becomes a temporary cyst after 59 contacts with G. mikimotoi while G. mikimotoi is killed after 19 contacts with H. circularisquama.

Thus, the strength of the inhibitory effect of H. circularisquama is about three times higher than that of G. mikimotoi. Furthermore, H. circularisquama survives as temporary cysts if its growth is suppressed in the presence of a high cell density of G. mikimotoi whereas G. mikimotoi died out in the bialgal cultures when the initial cell densities are at the same level. Therefore, H. circularisquama seems to have a superior survival strategy to G. mikimotoi considering the results of culture study obtained here. However, the present study has been conducted under fixed environmental conditions of temperature and light using a culture medium with artificially high nutrient levels. Further research will determine if the degree of inhibition between G. mikimotoi and H. circularisquama is affected by these environmental factors of temperature, light and nutrient levels.

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4.2. Growth simulation in bialgal cultures

The growth of H. circularisquama and G. mikimotoi in bialgal cultures was simulated using the following equations:

dx / dt5r x(1x 2x /K )x 2Axy5r x(1x 2(x1ay) /K )x (1) dy / dt5r y(1y 2y /K )y 2Bxy5r y(1y 2(bx1y) /K )y (2)

dz / dt5Axy5(ar /K )x x ?xy (3)

Here, x, y and z are the motile cell densities of H. circularisquama and G. mikimotoi, and immotile H. circularisquama, respectively. Then r and K are the growth rate andx x

carrying capacity of H. circularisquama, and r and K are the corresponding parametersy y

Eqs. (1) and (2) can be approximated with the following equations:

(ln xi112ln xi21) /(ti112ti21)5rx2r x /Kx i x2r ay /Kx i x (4) (ln yi112ln yi21) /(ti112ti21)5ry2r bx /Ky i y2r y /Ky i y (5) Here, x and y denote the observed cell densities at time t for H. circularisquama andi i i G. mikimotoi, respectively. When each species is cultured in a monoalgal culture, we can put a5b50. The logistic parameters were estimated by Eqs. (4) and (5) using the monoalgal culture data. Then the parameters a and b were calculated using bialgal culture data directly from Eqs. (4) and (5). Moreover, precise estimations of parameters

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a and b were carried out using the following function as a measure of agreement

between the observed and estimated growth of x, y and z.

2 2

* *

V(a,b)5

O

hln(x_i 1e)2ln(x )_i j 1

O

hln( y_i 1e)2ln( y )_i j

O

hln(zi 1e)2ln(z )i j (6)

Here, x , y and z refer to the observed motile cell densities of H. circularisquama andi i i G. mikimotoi, and immotile H. circularisquama, respectively. The parameters a and b

were changed from 0 to 500. For each set of a and b, the theoretical cell densities, x ,i

* *

236

constante(510 ) was introduced into Eq. (6). The most appropriate values of a and

b were determined when V(a,b) became minimum.

The carrying capacity for H. circularisquama (K ) and for G. mikimotoi (K ) wasx y

calculated 352 416 and 92 286 cells ml , respectively (Table 1). The growth rate was

21 21

estimated at 1.039 div. day for H. circularisquama, and 0.485 div. day for G.

mikimotoi which were calculated by the conversion from natural logarithms to

logarithms of base 2 since both species grow by binary fission (Table 1). The optimum values of a and b were 144 and 245, respectively, as indicated in Table 1. The growth patterns of H. circularisquama and G. mikimotoi calculated using these values of a and

b are given in Fig. 6. These growth curves are in good agreement with those obtained in

the culture experiments.

x5392 and y52.514. The estimated parameters show that this is the unstable equilibrium point because Kx,aK and bKy x.K (Iwasa, 1998). Consequently, in anyy

The degree of inhibition on H. circularisquama by G. mikimotoi was calculated at

29 21 21

3.4310 ml cells s (parameter A) and on G. mikimotoi by H. circularisquama at

29 21 21

11310 ml cells s (parameter B ), respectively (Table 1). Cell contact frequency to cause the death of G. mikimotoi and temporary cyst formation of H. circularisquama

Table 1

Estimated parameters

Carrying Growth rate (r) Interaction rate capacity (K )

21 21

(cells ml ) (h ) (divisions a or b A or B

21 21 21

day ) (ml cell s )

Heterocapsa circularisquama 352 416 0.030 1.039 144 3.4310

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growth of each species observed in bialgal cultures, (h) G. mikimotoi, (m) motile cells of H. circularisquama, (^) immotile cells of H. circularisquama.

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Fig. 7. Isoclines for which dx / dt50 and dy / dt50, and the trajectories of Heterocapsa circularisquama and

Gymnodinium mikimotoi under various initial cell densities. Areas (I)–(IV) are divided by the two lines of

H. circularisquama and G. mikimotoi increase; area IV: cell density of H. circularisquama decreases but that of G. mikimotoi increases.

1 / 2 2

F52 pcd xy (7)

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which a cell passed through a certain distance measured by a micrometer under an

21 21

inverted microscope, is 0.58 m h for H. circularisquama and 0.49 m h for G.

mikimotoi. If it is assumed that the cell diameter is 18mm and the swimming velocity is

21 27

0.5 m h for both species, theoretical cell contact frequency is calculated as 2310 xy

21 21

(cell ml s ). By comparing this value with parameters A and B, it is estimated that H.

circularisquama becomes a temporary cyst after 59 contacts with G. mikimotoi while G.

mikimotoi is killed after 19 contacts with H. circularisquama.

mikimotoi whereas G. mikimotoi died out in the bialgal cultures when the initial cell densities are at the same level. Therefore, H. circularisquama seems to have a superior survival strategy to G. mikimotoi considering the results of culture study obtained here. However, the present study has been conducted under fixed environmental conditions of temperature and light using a culture medium with artificially high nutrient levels. Further research will determine if the degree of inhibition between G. mikimotoi and H.

circularisquama is affected by these environmental factors of temperature, light and

nutrient levels.