- Email: [email protected]
Are models which explain the paradox of the plankton really different?
|WtlWlilil ELSEVIER
Ecological Modelling97 (1997) 247-251
Letter to the editor
Are models which explain the paradox of the plankton really different? E r n e s t o J. G o n z f i l e z * Universidad Central de Venezuela, Instituto de Biologla Experimental, Apartado 47106, Los Chaguaramos, Caracas 1041, Venezuela
Accepted 18 July 1996
Keywords: Paradox of the plankton; Equilibrium model; Non equilibrium model; Mixed model
The competitive exclusion principle states that species which directly compete cannot coexist (Hardin, 1960). According to this principle, in relative homogeneous environments (i.e. the wellmixed layers of lakes), few species with similar requirements should be found (Darley, 1982; Wetzel, 1983). All planktonic algae species are essentially phototrophic, with similar requirements that must be satisfied from their neighbour environments. Therefore, resource competition, specially for nutrients, should result in the elimination of all other species except those best adapted to use the limiting resources. However, in these environments we find the simultaneous dominance of many lacustrine phytoplankton species that show simultaneous population growth. This contradicts the competitive exclusion principle. The coexistence of more than 30 species of phytoplankton in
*Tel.: +58 2 7510111; fax: +58 2 7525897; e-mail: [email protected]
the same water body has been called the 'paradox of the plankton' (Hutchinson, 1961). According to Ghilarov (1984), after three decades since the Hutchinson's paper was published, traditional explanations such as the niche divergence or the environmental instability have not contributed to solve this paradox. To explain the paradox, many hypotheses have been issued and grouped in equilibrium and non equilibrium models. In this paper, I intend to search for similarities among some of these models, with the aim to contribute to the development of a mixed model. The Petersen's equilibrium model will be emphasized. It is an application of the equilibrium models of Le6n and Tumpson (1975) applied to plankton dynamics by Tilman (1982, 1986). Petersen (1975), suggests that several species of phytoplankton can coexist in true competitive equilibrium if they are collectively restricted from further growth by an array of different nutrients. This hypothesis requires that:
0304-3800/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0304-3800(96)01902-3
248
E.J. Gonz6lez / Ecological Modelling 97 (1997) 247-251
1. several nutrients are in relatively short supply 2. growth of each species are restricted by a single nutrient or a unique combination of several nutrients 3. different species possess unequal abilities for the uptake of the various nutrients Petersen's model uses elements established in the Monod equation of external nutrient control model:
where /~ = specific growth rate; #m = maximum specific growth rate; S = concentration of limiting resource; Ks = half saturation constant. The equilibrium concentration of the limiting nutrient (R*) can be obtained by rearrangement of terms in the previous equation (Sommer, 1986). Although the equation was derived for one species, it can be extended to include many competing species (Tilman, 1981): Di •Kij R* = (ri -- Di ) where R* = amount of nutrient j required by species i to have a reproductive rate equal to its mortality rate; ri;maximum per capita growth rate of species i (equivalent to/t); Kij -- half saturation constant for species i when limited by nutrient j; D i -----mortality rate of species i. At equilibrium conditions, the species with the lowest R* will competitively displace all the other species (Tilman, 1981; Darley, 1982; Ghilarov, 1984; Sommer, 1986; Grover, 1988). This R* is the basic element in the Petersen's equilibrium model (Fig. 1). The nutrient requirements of two competing species are indicated in the figure by the two vectors (Rll, RI2) and (RE1, R22), which represent the effect of uptake of the two different nutrients by species 1 and 2, respectively. Given any particular initial concentration of the two nutrients (S1, $2), they will be depleted along a trajectory parallel to (R H, RI2) by the growth of species 1 only, and along a trajectory parallel to (R21, R22) by the growth of species 2 only. A necessary requirement for the equilibrium is that (S~, $2) must fall somewhere in the shaded area between
(Rll, R12) and (R21, R22). If (SI, $2) lies above or below of shaded area, any combination of abundances of competing species will deplete only one nutrient to limiting levels. The survivor will be the species with the best ability in acquiring the depleted nutrient. Another requirement for this model is that each species will have the half saturation constant (Ki;) smaller than others acquiring at least one nutrient present in limiting amounts, and that for each species Kij and Rij be positively correlated. Many experiments which confirmed the equilibrium model were performed using nutrient concentrations which allowed the coexistence of several species of phytoplankton (Titman, 1976; Tilman, 1977; Tilman, 1981; Tilman et al., 1981). Other explanations are given by mathematical models, such as the Volterra type equations applied by Kolesov (1992). In contrast, non equilibrium models state that the competitive exclusion of species is avoided by some disturbing influences of the environment such as patchiness, seasonality, or predation (Ghilarov, 1984). Grenney et al. (1973), developed a mathematical model, derived from Monod's equation, to represent phytoplankton growth dynamics which can be considered as an example of the non equilibrium type. It describes the population dy-
(R21, R22)
is c,Es 2 xl
AI
ll
"'2 ' 1(21 KI I NUTRIENT I
Fig. 1. Conditions allowing equilibrium between competing species of phytoplankton. R0 represents the relative proportion of the biomass of species i contribuited by nutrient j; Kij is the transport constant, which determine the ability of each species to acquire a particular nutrient present in small concentration. ($1, $2) represents the ratio of nutrients in the system. Modified from Petersen (1975).
E.J. Gonz&lez /Ecological Modelling 97 (/997) 247-251
z0
249
FLOW RATES' HIGH Q
INTERMEDIATE Q
LOW Q
OE
Z~
8
-''---~
4 z
uJ E: I-.-
0
40
80
120
160
40
80 120 160 TIME (DAYS)
40
80
120
160 2 0 0
'3
z
SPECIES A -
SPECIES B - - -
Fig. 2. Competition between species A and B in the same environment and at several constant Q. C = 22.0 l~g - at/l. Modified from Grenney et al. (1973).
namics under competition conditions with a variable supply of a single nutrient. The Grenney et al. (1973) model portrays a system whose volume is constant and well-mixed and is kept at optimal temperature and light intensity, but in which a single nutrient is limiting. Furthermore, it includes three independent variables: time, incoming nutrient concentration (C) and flow rate (Q). The model might be considered as a simple representation of a completely mixed epilimnion above a strong thermocline. Q represents the transport rate of materials across the thermocline due to mixing and C is the nutrient concentration below the thermocline. Grenney et al. (1973) simulated the competition between two hypothetical species A and B which differed in their maximum growth (slight advantage for species A) and nutrient assimilation rates (slight advantage for species B). The computer program predicted that, at high flows of the limiting nutrient, species A excluded species B, whereas at low flows species B eliminated species A (Fig. 2). At intermediate Q both species coexisted. Also, when Q were temporally varied (pulses of nutrient), both species coexisted (Fig. 3). Varying the flow of the limiting nutrient, an interval for the coexistence of both species could be obtained (Fig. 4). Results obtained by Sommer (1985, 1986) and by Grover (1988) sustain this non equilibrium model. Sommer (1990), explains that limitation by N and P, which are rapidly recycled, appears to be discontinuous rather than continuous. In situ competition for these nutrients probably has more similarity with pulsed-state competition experiments than with steady state experiments. Accord-
ing to this author, the interrupted nature of P and N supply is an important finding with respect to Hutchinson's 'paradox of the plankton'. Deviations from steady state, such as periodic nutrient pulses (Sommer, 1985; Sommer, 1986; Grover, 1988), have shown that the number of coexisting species could be larger than the number of limiting resources.
1. Towards a mixed model
The aim of this paper is not to propose a model, but to stress some similarities among the elements of the equilibrium and non equilibrium models. Mainly, both types of models include ~)
12
lie
s-
.e...
t
4
r.- W :DO ZZ
o o ~
i
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I I
.
i
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*
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i i
I
!
s I
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I I
i
rr hi 0
o
' ;o' do' ,io' ,;o'zoo
TIME (DAYS) SPECIES A SPECIES B - - Fig. 3. Coexistence of the hypothetical species A and B in the same environment due the periodical step variations in flow Q. C 22.0/~g - at/1 (in this example), P = cycle period (in days) and h = duration of 'high' flow (in days). Modified from Grenney et al. (1973).
E.J. Gonzdlez/ Ecological Modelling 97 (1997) 247-251
250
Acknowledgements
50
4O
-
",.
I am very grateful with Dr Andrrs Carmona and Dr Abraham Levy who corrected the English version of this manuscript. I thank to Dr Aida de Infante and Dr Diego Rodriguez for their comments to improve the manuscript.
SPECIESA WINS
O ..J
u_ 30 "1(.9
20 SPECIES B WINS
o~ I0 0
I
I
I0
20
I
I
I
I
30
40
50
60
References 70
PERIOD (DAYS) Fig. 4. Region of coexistence for the hypothetical species A and B, as a result of various flow regimes. Modified from Grenney et al. (1973).
conditions of coexistence (shaded areas in Figs. 1 and 4). For instance, if the concentration of nutrients S~, $2 fluctuate in time, but always within determined intervals, i.e. in the shaded area from Fig. 1, the competing species could coexist. In this argument there is an element from Grenney et al. (1973) non equilibrium model: seasonality in the concentration of nutrients which could occur inside the region of coexistence showed in the Petersen's equilibrium model. In this regard, Tilman (1988) considered that if the nutrient supply varies in a defined pattern within the shaded area in Fig. 1, the species succession could occur. This represents a non equilibrium model with mathematical equilibrium elements. These arguments could lead to think that both types of models instead of being exclusive are complementary. This statement finds support in Tilman et al. (1981) asseveration that the natural world may not be in true equilibrium but includes non equilibrium situations. Although the equilibrium and non equilibrium models may be useful to solve Hutchinson's 'paradox of the plankton', a mixed model that uses elements from each kind may, perhaps, be more appropriate to explain the simultaneous coexistence of phytoplankton species in well-mixed layers of water bodies.
Darley, W.M., 1982. Algal Biology: A Physiological Approach. Blackwell, Oxford, 168 pp. Ghilarov, A.M., 1984. The paradox of the plankton reconsidered; or, why do species coexist? Oikos, 43: 46-52. Grenney, W.J., Bella, D.A. and Curl, H.C., 1973. A theoretical approach to interspecific competition in phytoplankton communities. Am. Nat., 107: 405-425. Grover, J.P., 1988. Dynamics of competition in a variable environment: experiments with two diatom species. Ecology, 69: 408-417. Hardin, G., 1960. The competitive exclusion principle. Science, 131: 1292-1297. Hutchinson, G.E., 1961. The paradox of the plankton. Am. Nat., 95: 137-145. Kolesov, Yu.S., 1992. Explanation of the plankton paradox. Biophysics, 37: 1015-1016. Le6n, J.A. and Tumpson, D.B., 1975. Competition between two species for two complementary or substitutable resources. J. Theor. Biol., 50: 185-201. Petersen, R., 1975. The paradox of the plankton: an equilibrium hypothesis. Am. Nat., 109: 35-49. Sommer, U., 1985. Comparison between steady state and non-steady state competition: experiments with natural phytoplankton. Limnol. Oceanogr., 30: 335-346. Sommer, U., 1986. Phytoplankton competition along a gradiente of dilution rates. Oecologia, 68: 503-506. Sommer, U., 1990. Phytoplankton nutrient nutrient competition from laboratory to lake. In: J.B. Grace and D. Tilman (Editors), Perspectives on Plant Competition. Academic Press, San Diego, pp. 193-213. Tilman, D., 1977. Resource competition between planktonic algae: an experimental and theoretical approach. Ecology, 58: 338-348. Tilman, D., 1981. Test of resource competition theory using four species of Lake Michigan algae. Ecology, 62: 802815. Tilman, D., 1982. Resource Competition and Community Structure. Princeton University Press, N J, 296 pp. Tilman, D., 1986. Resources, competition and dynamics of plant communities. In: M.J. Crawley (Editor), Plant Ecology. Blackwell, Oxford, pp. 51-75. Tilman, D., 1988. Dynamics and structure of plant communities. Monographs in Population Biology 26. Princeton University Press, N J, 360 pp.
E.J. Gonzddez/ Ecological Modelling 97 (1997) 247-251 Tilman, D., Mattson, M. and Langer, S., 1981. Competition and nutrient kinetics along a temperature gradient: an experimental test of a mechanistic approach to niche theory. Limnol. Oceanogr., 26: 10201033.
251
Titman, D., 1976. Ecological competition between algae: experimental confirmation of resource-based competition theory. Science, 192: 463-465. Wetzel, R., 1983. Limnology (2nd edition). Saunders, Philadelphia, 762 pp.
Ecological Modelling97 (1997) 247-251
Letter to the editor
Are models which explain the paradox of the plankton really different? E r n e s t o J. G o n z f i l e z * Universidad Central de Venezuela, Instituto de Biologla Experimental, Apartado 47106, Los Chaguaramos, Caracas 1041, Venezuela
Accepted 18 July 1996
Keywords: Paradox of the plankton; Equilibrium model; Non equilibrium model; Mixed model
The competitive exclusion principle states that species which directly compete cannot coexist (Hardin, 1960). According to this principle, in relative homogeneous environments (i.e. the wellmixed layers of lakes), few species with similar requirements should be found (Darley, 1982; Wetzel, 1983). All planktonic algae species are essentially phototrophic, with similar requirements that must be satisfied from their neighbour environments. Therefore, resource competition, specially for nutrients, should result in the elimination of all other species except those best adapted to use the limiting resources. However, in these environments we find the simultaneous dominance of many lacustrine phytoplankton species that show simultaneous population growth. This contradicts the competitive exclusion principle. The coexistence of more than 30 species of phytoplankton in
*Tel.: +58 2 7510111; fax: +58 2 7525897; e-mail: [email protected]
the same water body has been called the 'paradox of the plankton' (Hutchinson, 1961). According to Ghilarov (1984), after three decades since the Hutchinson's paper was published, traditional explanations such as the niche divergence or the environmental instability have not contributed to solve this paradox. To explain the paradox, many hypotheses have been issued and grouped in equilibrium and non equilibrium models. In this paper, I intend to search for similarities among some of these models, with the aim to contribute to the development of a mixed model. The Petersen's equilibrium model will be emphasized. It is an application of the equilibrium models of Le6n and Tumpson (1975) applied to plankton dynamics by Tilman (1982, 1986). Petersen (1975), suggests that several species of phytoplankton can coexist in true competitive equilibrium if they are collectively restricted from further growth by an array of different nutrients. This hypothesis requires that:
0304-3800/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0304-3800(96)01902-3
248
E.J. Gonz6lez / Ecological Modelling 97 (1997) 247-251
1. several nutrients are in relatively short supply 2. growth of each species are restricted by a single nutrient or a unique combination of several nutrients 3. different species possess unequal abilities for the uptake of the various nutrients Petersen's model uses elements established in the Monod equation of external nutrient control model:
where /~ = specific growth rate; #m = maximum specific growth rate; S = concentration of limiting resource; Ks = half saturation constant. The equilibrium concentration of the limiting nutrient (R*) can be obtained by rearrangement of terms in the previous equation (Sommer, 1986). Although the equation was derived for one species, it can be extended to include many competing species (Tilman, 1981): Di •Kij R* = (ri -- Di ) where R* = amount of nutrient j required by species i to have a reproductive rate equal to its mortality rate; ri;maximum per capita growth rate of species i (equivalent to/t); Kij -- half saturation constant for species i when limited by nutrient j; D i -----mortality rate of species i. At equilibrium conditions, the species with the lowest R* will competitively displace all the other species (Tilman, 1981; Darley, 1982; Ghilarov, 1984; Sommer, 1986; Grover, 1988). This R* is the basic element in the Petersen's equilibrium model (Fig. 1). The nutrient requirements of two competing species are indicated in the figure by the two vectors (Rll, RI2) and (RE1, R22), which represent the effect of uptake of the two different nutrients by species 1 and 2, respectively. Given any particular initial concentration of the two nutrients (S1, $2), they will be depleted along a trajectory parallel to (R H, RI2) by the growth of species 1 only, and along a trajectory parallel to (R21, R22) by the growth of species 2 only. A necessary requirement for the equilibrium is that (S~, $2) must fall somewhere in the shaded area between
(Rll, R12) and (R21, R22). If (SI, $2) lies above or below of shaded area, any combination of abundances of competing species will deplete only one nutrient to limiting levels. The survivor will be the species with the best ability in acquiring the depleted nutrient. Another requirement for this model is that each species will have the half saturation constant (Ki;) smaller than others acquiring at least one nutrient present in limiting amounts, and that for each species Kij and Rij be positively correlated. Many experiments which confirmed the equilibrium model were performed using nutrient concentrations which allowed the coexistence of several species of phytoplankton (Titman, 1976; Tilman, 1977; Tilman, 1981; Tilman et al., 1981). Other explanations are given by mathematical models, such as the Volterra type equations applied by Kolesov (1992). In contrast, non equilibrium models state that the competitive exclusion of species is avoided by some disturbing influences of the environment such as patchiness, seasonality, or predation (Ghilarov, 1984). Grenney et al. (1973), developed a mathematical model, derived from Monod's equation, to represent phytoplankton growth dynamics which can be considered as an example of the non equilibrium type. It describes the population dy-
(R21, R22)
is c,Es 2 xl
AI
ll
"'2 ' 1(21 KI I NUTRIENT I
Fig. 1. Conditions allowing equilibrium between competing species of phytoplankton. R0 represents the relative proportion of the biomass of species i contribuited by nutrient j; Kij is the transport constant, which determine the ability of each species to acquire a particular nutrient present in small concentration. ($1, $2) represents the ratio of nutrients in the system. Modified from Petersen (1975).
E.J. Gonz&lez /Ecological Modelling 97 (/997) 247-251
z0
249
FLOW RATES' HIGH Q
INTERMEDIATE Q
LOW Q
OE
Z~
8
-''---~
4 z
uJ E: I-.-
0
40
80
120
160
40
80 120 160 TIME (DAYS)
40
80
120
160 2 0 0
'3
z
SPECIES A -
SPECIES B - - -
Fig. 2. Competition between species A and B in the same environment and at several constant Q. C = 22.0 l~g - at/l. Modified from Grenney et al. (1973).
namics under competition conditions with a variable supply of a single nutrient. The Grenney et al. (1973) model portrays a system whose volume is constant and well-mixed and is kept at optimal temperature and light intensity, but in which a single nutrient is limiting. Furthermore, it includes three independent variables: time, incoming nutrient concentration (C) and flow rate (Q). The model might be considered as a simple representation of a completely mixed epilimnion above a strong thermocline. Q represents the transport rate of materials across the thermocline due to mixing and C is the nutrient concentration below the thermocline. Grenney et al. (1973) simulated the competition between two hypothetical species A and B which differed in their maximum growth (slight advantage for species A) and nutrient assimilation rates (slight advantage for species B). The computer program predicted that, at high flows of the limiting nutrient, species A excluded species B, whereas at low flows species B eliminated species A (Fig. 2). At intermediate Q both species coexisted. Also, when Q were temporally varied (pulses of nutrient), both species coexisted (Fig. 3). Varying the flow of the limiting nutrient, an interval for the coexistence of both species could be obtained (Fig. 4). Results obtained by Sommer (1985, 1986) and by Grover (1988) sustain this non equilibrium model. Sommer (1990), explains that limitation by N and P, which are rapidly recycled, appears to be discontinuous rather than continuous. In situ competition for these nutrients probably has more similarity with pulsed-state competition experiments than with steady state experiments. Accord-
ing to this author, the interrupted nature of P and N supply is an important finding with respect to Hutchinson's 'paradox of the plankton'. Deviations from steady state, such as periodic nutrient pulses (Sommer, 1985; Sommer, 1986; Grover, 1988), have shown that the number of coexisting species could be larger than the number of limiting resources.
1. Towards a mixed model
The aim of this paper is not to propose a model, but to stress some similarities among the elements of the equilibrium and non equilibrium models. Mainly, both types of models include ~)
12
lie
s-
.e...
t
4
r.- W :DO ZZ
o o ~
i
0 I.O
I I
.
i
I
*
I t
I
I
I
i i
I
!
s I
|
I I
i
rr hi 0
o
' ;o' do' ,io' ,;o'zoo
TIME (DAYS) SPECIES A SPECIES B - - Fig. 3. Coexistence of the hypothetical species A and B in the same environment due the periodical step variations in flow Q. C 22.0/~g - at/1 (in this example), P = cycle period (in days) and h = duration of 'high' flow (in days). Modified from Grenney et al. (1973).
E.J. Gonzdlez/ Ecological Modelling 97 (1997) 247-251
250
Acknowledgements
50
4O
-
",.
I am very grateful with Dr Andrrs Carmona and Dr Abraham Levy who corrected the English version of this manuscript. I thank to Dr Aida de Infante and Dr Diego Rodriguez for their comments to improve the manuscript.
SPECIESA WINS
O ..J
u_ 30 "1(.9
20 SPECIES B WINS
o~ I0 0
I
I
I0
20
I
I
I
I
30
40
50
60
References 70
PERIOD (DAYS) Fig. 4. Region of coexistence for the hypothetical species A and B, as a result of various flow regimes. Modified from Grenney et al. (1973).
conditions of coexistence (shaded areas in Figs. 1 and 4). For instance, if the concentration of nutrients S~, $2 fluctuate in time, but always within determined intervals, i.e. in the shaded area from Fig. 1, the competing species could coexist. In this argument there is an element from Grenney et al. (1973) non equilibrium model: seasonality in the concentration of nutrients which could occur inside the region of coexistence showed in the Petersen's equilibrium model. In this regard, Tilman (1988) considered that if the nutrient supply varies in a defined pattern within the shaded area in Fig. 1, the species succession could occur. This represents a non equilibrium model with mathematical equilibrium elements. These arguments could lead to think that both types of models instead of being exclusive are complementary. This statement finds support in Tilman et al. (1981) asseveration that the natural world may not be in true equilibrium but includes non equilibrium situations. Although the equilibrium and non equilibrium models may be useful to solve Hutchinson's 'paradox of the plankton', a mixed model that uses elements from each kind may, perhaps, be more appropriate to explain the simultaneous coexistence of phytoplankton species in well-mixed layers of water bodies.
Darley, W.M., 1982. Algal Biology: A Physiological Approach. Blackwell, Oxford, 168 pp. Ghilarov, A.M., 1984. The paradox of the plankton reconsidered; or, why do species coexist? Oikos, 43: 46-52. Grenney, W.J., Bella, D.A. and Curl, H.C., 1973. A theoretical approach to interspecific competition in phytoplankton communities. Am. Nat., 107: 405-425. Grover, J.P., 1988. Dynamics of competition in a variable environment: experiments with two diatom species. Ecology, 69: 408-417. Hardin, G., 1960. The competitive exclusion principle. Science, 131: 1292-1297. Hutchinson, G.E., 1961. The paradox of the plankton. Am. Nat., 95: 137-145. Kolesov, Yu.S., 1992. Explanation of the plankton paradox. Biophysics, 37: 1015-1016. Le6n, J.A. and Tumpson, D.B., 1975. Competition between two species for two complementary or substitutable resources. J. Theor. Biol., 50: 185-201. Petersen, R., 1975. The paradox of the plankton: an equilibrium hypothesis. Am. Nat., 109: 35-49. Sommer, U., 1985. Comparison between steady state and non-steady state competition: experiments with natural phytoplankton. Limnol. Oceanogr., 30: 335-346. Sommer, U., 1986. Phytoplankton competition along a gradiente of dilution rates. Oecologia, 68: 503-506. Sommer, U., 1990. Phytoplankton nutrient nutrient competition from laboratory to lake. In: J.B. Grace and D. Tilman (Editors), Perspectives on Plant Competition. Academic Press, San Diego, pp. 193-213. Tilman, D., 1977. Resource competition between planktonic algae: an experimental and theoretical approach. Ecology, 58: 338-348. Tilman, D., 1981. Test of resource competition theory using four species of Lake Michigan algae. Ecology, 62: 802815. Tilman, D., 1982. Resource Competition and Community Structure. Princeton University Press, N J, 296 pp. Tilman, D., 1986. Resources, competition and dynamics of plant communities. In: M.J. Crawley (Editor), Plant Ecology. Blackwell, Oxford, pp. 51-75. Tilman, D., 1988. Dynamics and structure of plant communities. Monographs in Population Biology 26. Princeton University Press, N J, 360 pp.
E.J. Gonzddez/ Ecological Modelling 97 (1997) 247-251 Tilman, D., Mattson, M. and Langer, S., 1981. Competition and nutrient kinetics along a temperature gradient: an experimental test of a mechanistic approach to niche theory. Limnol. Oceanogr., 26: 10201033.
251
Titman, D., 1976. Ecological competition between algae: experimental confirmation of resource-based competition theory. Science, 192: 463-465. Wetzel, R., 1983. Limnology (2nd edition). Saunders, Philadelphia, 762 pp.