Ecological Modelling 134 (2000) 245 – 274
www.elsevier.com/locate/ecolmodel
Copepod food-quality threshold as a mechanism influencing
phytoplankton succession and accumulation of biomass, and
secondary productivity: a modeling study with management
implications
D.L. Roelke *
Department of Wildlife and Fisheries Sciences, Texas A&M Uni6ersity, College Station, TX 77843 -2258, USA
Received 14 September 1999; received in revised form 2 February 2000; accepted 6 June 2000
Abstract
Development of proactive management schemes may be necessary to combat the apparent worldwide increase in
harmful algal blooms. Design of such schemes will require a thorough understanding of bloom-initiating processes in
an ecosystem context. To further explore potential synergistic effects between abiotic and biotic processes impacting
plankton community dynamics a detailed numerical model was developed and tested. The model featured multiple
growth limiting resources (nitrogen, phosphorus, silica, light), multiple phytoplankton groups (P-specialist, N-specialist, intermediate group), aspects of the microbial loop (labile dissolved organic nitrogen, bacteria, microflagellates,
ciliates), and a capstone predator (copepods). Model simulations illuminated the potential role of food-quality
threshold as it effected initiation of an algal bloom. The mechanism controlling whether a bloom would occur and
secondary productivity cease was the timing of the onset of bottom – up control (nutrient limitation) relative to
top–down control (high grazing pressure). Simulations where top – down control occurred before bottom – up control
were characteristic of Lotka–Volterra type behavior. However, during simulations where top – down control began
after bottom–up control an algal bloom resulted and secondary productivity ceased. This occurred because at the
time of maximum grazing activity the N-content of one of the phytoplankton groups was below the food-quality
threshold for copepods. Consequently, copepod growth was not great enough to offset losses. As a result, the
copepod population was eliminated and an algal bloom ensued. The timing of the onset of bottom – up and top – down
control was sensitive to some abiotic conditions that included magnitude, mode, and ratio of nutrient loading.
Through manipulation of these abiotic processes, it was possible to maintain phytoplankton species diversity, enhance
secondary productivity, and prevent an algal bloom. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Food-quality threshold; Plankton dynamics; Copepod growth
* Tel.: +1-409-8450169.
E-mail address: [email protected] (D.L. Roelke).
0304-3800/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 3 8 0 0 ( 0 0 ) 0 0 3 4 6 - X
246
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
1. Introduction
Abiotic and biotic processes influencing the succession of species within phytoplankton communities and accumulation of algal biomass are
many and their synergism complex (Sommer et
al., 1986; Odum et al., 1995; Roelke et al., 1997;
Breitburg et al., 1999). With the apparent worldwide increase in harmful algal blooms and resulting diminished quality of aquatic ecosystems (see
Anderson and Garrison, 1997), there is a need for
implementation
of
proactive
management
schemes aimed at sustaining or restoring the quality of the natural environment. Detailed models
built on our understanding of the mechanisms
that underlie phytoplankton community succession, accumulation of algal biomass, and triggering of algal blooms must guide the design of such
management schemes. Attempts at modeling
planktonic ecosystems to this degree, however,
have been few (Franks, 1997).
Many models exist, conceptual and numerical,
which elucidate mechanisms underlying phytoplankton community succession (Tilman, 1977;
Ebenhoh, 1988; Sommer, 1989a,b; Montealegre et
al., 1995; Roelke et al., 1999). From an ecosystem
perspective, these models are appealing because
most consider multiple phytoplankton species,
multiple limiting resources, and preferential grazing effects, thereby presenting a more holistic view
of the natural environment. To explain occurrence
of algal blooms in the context of these models,
however, mechanisms that either reduce grazing
losses of a specific phytoplankton species, or inhibit growth of competing algae, must be invoked.
Such mechanisms are not always well understood
and the formulations used to incorporate these
processes into models may not be accurate over a
wide range of environmental conditions. Regarding conceptual models, they are further limited in
that they do not lend themselves to addressing the
influence of physical processes on plankton community dynamics.
Other modeling efforts, which do not incorporate mechanisms that reduce grazing or inhibit
growth of competitors, have demonstrated mathematically that algal blooms can occur simply
through a decoupling of grazing processes and
algal growth (Kishi and Ikeda, 1986; Truscott,
1995; Hessen and Bjerkeng, 1997). This can occur
through differential physical mixing or migration
between phytoplankton and zooplankton, as well
as through shifts in resource availability coupled
to differential response times between phytoplankton and zooplankton. These models are appealing because they do not ‘force’ blooms.
Rather, the mechanisms underlying bloom formation are a result of synergistic effects between well
understood biotic and abiotic processes. Most
numerical models of this nature, however, do not
incorporate multiple species, multiple limiting resources, or preferential grazing processes. As a
result, they are less representative of the natural
environment.
The primary goal of this research was to develop a more complex numerical model where
both abiotic and biotic processes controlled
plankton dynamics, and to use the model to explore synergistic effects of multiple mechanisms
known to influence phytoplankton community
succession, accumulation of algal biomass, and
secondary productivity. Emphasis was placed on
the role of nutrient loading magnitude, mode of
nutrient loading, and the ratio of loaded nutrients
because they may represent the most feasible of
plankton management options. It was not the
intent of this research to produce a predictive
model, i.e. a tool for design of management
schemes. Rather, the intent was to generate a tool
to be used to elucidate potential algal bloom
mechanisms and determine sensitivity of such
mechanisms to various abiotic and biotic processes. It is the hope of the investigator, however,
that future models built from the model presented
here will be tailored to target systems, and perhaps useful for management purposes. Reference
to the parameterization of the model is incorporated in Appendix A.
2. Basis of model design
Although the following model was not designed
for predictive purposes, it still had to behave in a
manner reasonable to the natural environment.
Therefore, the model was constructed based on
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
prior knowledge of a natural system (Roelke,
1997; Roelke et al., 1997), the Nueces River estuary (NRE). Notable features of NRE at the times
of sampling were that the nutrient inputs from the
Nueces River and a nearby sewage treatment
plant eclipsed nutrient inputs from the sediments,
and that the system was vertically well mixed.
Therefore, to represent NRE a box model was
developed that did not incorporate sediment effects. Because inorganic nitrogen species (N),
phosphate (P), and silicate (Si) appeared to influence the composition of the phytoplankton community in some parts of NRE, they were
incorporated in the model. In addition, the hydrology of NRE influenced plankton community
dynamics. To account for this, hydraulic residence
time in the form of advective inputs and losses
were built into the model.
It was not possible to include a separate category for all of the algal groups found in NRE and
still parameterize them in the context of the model
(see Nielsen, 1994). Instead, three functional
groups were developed, an N-specialist, a P-specialist, and an intermediate group. The parameterization of the three functional groups were mostly
based on a dinoflagellate, Prorocentrum minimum
(Sciandra, 1991), a green alga, Selenastrum minutum (Elrifi and Turpin, 1985), and a diatom,
Skeletonema costatum (DeManche et al., 1979),
respectively. Regarding N- and P-related parameters, the differential equations and parameter values used were from a previous modeling study
(Roelke et al., 1999). These equations were appealing because they described growth as function
of the cell-quota (Droop, 1973, 1983), nutrient
uptake as a function of resource availability and
cell starvation status (Zevenboom and Mur, 1979;
Goldman and Glibert, 1982; Riegman and Mur,
1984), and luxury consumption of nutrients as a
function of eventual limiting and non-limiting nutrients (Zonneveld, 1996). To better characterize
the phytoplankton groups additional equations
were added to account for light variability, silica
availability (for the intermediate group only),
grazing susceptibility, mortality, respiration and
exudation.
247
Not sampled directly in NRE, but considered
an important feature of foodwebs in general, was
the microbial loop. The role of bacteria as remineralizers of, and competitors for, inorganic nutrients is well documented. Furthermore, the role
of the microbial loop in plankton dynamics,
whether viewed as an alternative pathway for
nutrient transfer to higher trophic levels or as a
mechanism returning nutrients to lower trophic
levels, is important (Fuhrman, 1992). Therefore,
the microbial loop was built into the model and
was represented by including pools representative
of labile dissolved organic nitrogen (DON), bacteria, microflagellates, and ciliates.
Larger zooplankton were represented in the
model by including a copepod pool, which was
the capstone predator in the model, i.e. they were
able to graze on the phytoplankton groups and
the ciliate group. Copepods were selected as the
capstone predator because of their abundance in
an adjacent ecosystem, the Nueces Bay, their
known ability to crop primary productivity in
estuaries, and their relative dominance in coastal
ecosystems over other large zooplankton, e.g.
cladocerans (Dagg et al., 1991; Buskey, 1993;
Horne and Goldman, 1994). The influence of a
‘higher trophic’ level that fed on the copepods and
ciliates was incorporated in the model, but this
pool did not have a biomass component.
Throughout the model presentation the subscripts i and j were used in many of the equations.
Each had a value between 1 and 3 and represented different pools of the model as follows:
i= 1, intermediate algae group; i= 2, P-specialist;
i= 3, N-specialist; j = 1,copepods; j = 2, ciliates,
and j= 3, microflagellates. Subscript notation was
also used to identify a term with a specific
parameter
and
currency.
For
example,
ExcertionGP signifies the processes of excretion
due to grazers (G) in regards to phosphorus (P).
Some of the equations in the model were designed
to conserve currencies (N, P, Si) of the model. For
example, respiration losses to bacteria in the form
of cells l − 1 day − 1 were balanced with a loss of N
from this pool in the form of mmol N l − 1 day − 1,
which is defined in model as remineralization of
N.
248
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
A graphical representation of the pools comprising the model and the interactions between the
pools is shown in Fig. 1. The differential equations are first shown with descriptive terms, followed by the equations that define each of the
terms. Values assigned to parameters are referenced in Appendix A. The model is solved using
an ordinary differential equation solver (Matlab™) that is based on fourth-order Runge –
Kutta methods (The MathWorks 1997).
3. Differential equations of the model with
descriptive terms
3.1. Phytoplankton cell concentration (i= 1, 2, 3)
dfi
=Growthfi − Respirationfi − Mortalityfi
dt
− Grazingfi − Advectionfi
(1)
Fig. 1. Graphical representation of the pools comprising the model and the interactions between the pools. Features of the model
included multiple limiting resources, multiple phytoplankton groups, the microbial loop, and a capstone predator. The effects of
irradiance and advection are not shown.
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
3.9. Labile organic N
3.2. Phytoplankton N cell-quota (i= 1, 2, 3)
dQfiN
=UptakefiN − DilutionfiN
dt
(2)
dDON
= SloppyG1DON + EgestionGDON
dt
+ ExudationfDON + MortalityfDON
3.3. Phytoplankton P cell-quota (i= 1, 2, 3)
dQfiP
=UptakefiP − DilutionfiP
dt
249
− UptakeBDON 9 AdvectionDON
(9)
(3)
4. Mathematics behind the descriptive terms
3.4. Bacteria
4.1. Phytoplankton growth
dB
=GrowthB −RespirationB −GrazingB
dt
−AdvectionB
(4)
3.5. Zooplankton (j= 1, 2, 3)
dGj
=GrowthGj − RespirationGj −MortalityGj
dt
−GrazingGj − AdvectionGj
Growthfi = mfifi
(5)
3.6. Dissol6ed inorganic N
dN
=RemineralizationBN +ExcretionGN
dt
+ MortalityGN −UptakefN,BN
9 AdvectionN
(6)
3.7. Dissol6ed inorganic P
dP
=RemineralizationBP +SloppyG 1P
dt
+ MortalityfP,GP +ExudationfP
(7)
3.8. Dissol6ed inorganic Si
dSi
=SloppyG1Si +EgestionGSi +Exudationf 1Si
dt
+ Mortalityf 1Si −Uptakef 1Si
9 AdvectionSi
(8)
(10)
where mfi is the specific growth rate of the group
(day − 1) and fi is the cell concentration of the
group (cells l − 1). The specific growth rate was a
function of intracellular N and P, similar to previous findings (Droop, 1983; Legovic and Cruzado,
1997), ambient Si concentration (for the intermediate group only), and irradiance. The equations
for specific growth rate regarding intracellular N
and P were identical to those of Roelke et al.
(1999).
For the intermediate group, which was based
on a diatom, the specific growth rate as a function
of ambient Si concentration was expressed with:
mf 1Si = mmax,f 1Si
+ ExcretionGP +EgestionGP
− UptakefP,BP 9AdvectionP
Phytoplankton growth rate was a function of
available nutrients and light similar to previous
modeling studies (Somlyody and Koncsos, 1991;
Montealegre et al., 1995; Legovic and Cruzado,
1997; Roelke et al., 1999). Growth for each group
(cells l − 1 day − 1) was expressed as:
Si
kf 1Si + Si
(11)
where mf 1Si is the Si-limited specific growth rate,
mmax,f 1Si is the maximum Si-limited specific
growth rate, Si is the ambient concentration of Si
(mmol Si l − 1), and kf 1Si is the half saturation
constant for Si-dependent growth (mmol Si l − 1).
Because specific growth rate has not been linked
to the Si content of diatom cells, a standard
Monod relationship (Monod, 1950) was used instead of a cell-quota formulation.
Specific growth rate as a function of irradiance
(day − 1) for each of the phytoplankton groups
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
250
followed a previous formulation (Platt, 1986):
Vfi =Vmax,fi (1− e
− Af
i
)
(12)
where Vfi is the light-dependent specific growth
rate (day − 1), Vmax,fi is the light-dependent maximum specific growth rate (day − 1) and the scalar
factor, Afi, was defined as:
afiI
Afi =
Vmax,fi
(15)
where rfi is a group specific scalar factor. Setting
respiration equal to a fraction of the production
was suggested elsewhere (Parsons et al., 1984;
Geider, 1992).
4.3. Phytoplankton mortality
(13)
where afi was the slope of the photosynthesis – irradiance curve (cm2 s quanta − 1 day − 1) for each
group and the irradiance was designated with the
letter I (quanta cm − 2 s − 1), and other symbols
were the same as defined Previously. The equations used to determine irradiance in the model
accounted for the influence of depth and light
attenuation in the water column, location on the
surface of the Earth, time of day and year, and
cloud cover (Brock, 1981; Montealegre et al.,
1995). The photoinhibition factor was dropped
from Eq. (12). For the purposes of this
manuscript the maximum irradiance intensities
were considered non-inhibiting.
The specific growth rate for each phytoplankton group was then determined using Liebig’s
Law of the Minimum (DeBaar, 1994; Legovic and
Cruzado, 1997):
mfi =MIN(mfiN, mfiP, mfiSi, Vfi )
Respirationfi = rfi Growthfi
Mechanisms influencing phytoplankton mortality processes are not well understood (Walsh,
1983; Fasham et al., 1990). For example, parasitism by viruses, bacteria, protozoa, and fungi
have been observed to terminate phytoplankton
blooms (Shilo, 1971; Fay, 1983; Donk, 1989), yet
factors effecting the growth and proliferation of
these parasites are not well known. Therefore, the
example of a previous model (Fasham et al.,
1990) was followed and mortality (cells l − 1
day − 1) was made a function of a specific loss rate
and cell concentration using:
Mortalityfi = mfifi
(16)
where mfi is a group specific mortality rate
(day − 1) and other symbols were the same as
defined previously.
4.4. Phytoplankton grazing losses
(14)
where mfiN and mfiP are the N- and P-limited
specific growth rate (day − 1), respectively, and
other symbols are the same as defined previously.
For the case of non-siliceous phytoplankton mSi
was not part of Eq. (14).
4.2. Phytoplankton respiration
Phytoplankton respiration is a complex process
relating to irradiance, nutrient availability, nutritional status of the cell, and temperature (Riley,
1946; Geider, 1992). Modeling phytoplankton respiration as a function of these parameters was
beyond the scope of this paper. Instead a simplistic formulation was used where the loss to each
phytoplankton group due to respiration (cells l − 1
day − 1) was made a fraction of the phytoplankton
group’s growth, and was depicted by:
The loss to each phytoplankton group due to
grazing from copepods (cells l − 1 day − 1) was a
function of the copepod grazing rate and concentration, and was expressed with:
Grazingfi =
g1G1
QfixV,fi
(17)
where g1 was the copepod growth rate in terms of
volume of prey (mm3 individual − 1 day − 1), G1 was
the concentration of copepods (individuals l − 1),
and QfixV,fi was the fixed cellular volume of the
phytoplankton group (mm3 cell − 1). To simulate
vertical migration behavior of copepods (see
Horne and Goldman, 1994), losses to phytoplankton due to copepod grazing only occurred during
night-time conditions. Copepod growth rate will
be discussed in more detail with the zooplankton
equations.
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
4.5. Phytoplankton uptake and dilution of
inorganic N and P
4.7. Bacterial respiration
The equations describing uptake of N and P,
and cellular dilution are identical to those reported in Roelke et al. (1999). Uptake rates for N
and P were not linked to irradiance. To prevent
unrealistic accumulation of N and P within phytoplankton cells during night-time conditions, when
growth was zero, uptake of N and P only occurred during day-time conditions.
4.6. Bacterial growth
Growth of bacteria (cells l − 1 day − 1) was a
function of the bacterial growth rate and concentration, and was expressed with:
GrowthB = mBB
(18)
where mB is the specific growth rate of the bacteria
(day − 1) and B is the concentration of bacteria
(cells l − 1). By using this formulation, growth of
the bacteria population was instantaneous, unlike
the phytoplankton groups. The bacterial specific
growth rate was dependent on the concentrations
of ambient N, DON, and P, and a relationship
between total N and P using Liebig’s Law of the
Minimum (DeBaar, 1994). The N-and P-dependent specific growth rates of bacteria were determined using:
mBN =mmax,B
N+ DON
)
kBN +N + DON
(19)
mBP =mmax,B
P
kBP + P
(20)
mB =MIN(mBN, mBP)
251
(21)
where mmax,B is the maximum bacterial specific
growth rate (day − 1), kBN and kBP were the half
saturation constants for bacterial uptake of N and
DON combined, and P (mmol N/DON l − 1, mmol
P l − 1), DON was the ambient concentration of
labile dissolved organic N (mmol DON l − 1), and
all other symbols were the same as previously
defined. Using a Monod formulation to relate
bacteria growth to ambient nutrient availability
was suggested elsewhere (Fasham et al., 1990).
Loss from the bacteria pool due to respiration
(cells l − 1 day − 1) was dependent on bacterial
growth and biomass and was expressed with:
RespirationB = r 1BGrowthB + r 2BB
(22)
where r 1B is the growth dependent respiration
(unitless), r 2B was the biomass dependent respiration (day − 1), and all other symbols were the same
as previously defined. Bacterial respiration was
described with two terms because each is a function of different processes. For example, when
bacteria growth was high the respiration loss was
higher, which represented greater metabolic activity due to cell division. When growth was near
zero, there was still a respiration loss that was a
function of cell maintenance processes, but it was
lower.
4.8. Bacteria grazing losses
The loss of bacteria due to grazing (cells l − 1
day − 1) was a function of the grazing rate and the
concentration of the microflagellate group, and
was expressed with:
GrazingB =
g3G3
QfixV,B
(23)
where g3 is the microflagellate growth rate in
terms of volume of bacteria (mm3 individual − 1
day − 1), G3 is the concentration of microflagellates
(cells l − 1), and QfixV,B is the fixed volume of a
bacterium (mm3 cell − 1).
4.9. Zooplankton growth
Growth of each zooplankton group (individuals
l − 1 day − 1) was determined by applying Liebig’s
Law of the Minimum to the total N and P
ingested relative to the fixed intracellular N and P
composition of the zooplankton group using:
GrowthGj = MIN
IngestionGjN IngestionGjP
,
Qfix,GjN
Qfix,GjP
(24)
where Qfix,GjN and Qfix,GjP are the fixed N and P
intracellular composition of each zooplankton
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
252
group (mmol N individual − 1, mmol P
individual − 1). The ingestion factors will be discussed next. By using this formulation copepod
population growth was instantaneous, i.e. development of cohorts was not incorporated into the
model, as in previous models (Nielsen, 1994; Norberg and DeAngelis, 1997).
Total N, P and Si ingested (mmol N l − 1 day − 1,
mmol P l − 1 day − 1, mmol Si l − 1 day − 1) for copepods was a function of the copepod grazing rate
and concentration, and a sloppy feeding correction, and was determined using:
g1G1QfiN g1G1Qfix,G 2N
+
QfixV,G 2
i = 1 QfixV,fi
3
IngestionG 1N = %
(1− x)
g1G1QfiP g1G1Qfix,G 2P
+
QfixV,G 2
i = 1 QfixV,fi
3
IngestionG 1P = %
(25)
(26)
g1G1Qfix,f 1Si
(1 − x)
QfixV,f 1
(27)
respectively, where QfiN and QfiP are the N and
P cell-quota of the phytoplankton groups (mmol
cell − 1), QfixV,G 2 is the fixed cellular volume of the
ciliate group (mm3 individual − 1), x is a sloppy
feeding constant specific to copepods (unitless),
Qfix,f 1Si is the fixed Si content of the intermediate
group, and all other symbols were the same as
defined previously.
Equations describing ingestion of N and P for
ciliates and microflagellates were more simplistic
because each only had one source of prey. For
ciliates the equations were:
g2G2Qfix,G 3N
QfixV,G 3
(28)
g2G2Qfix,G 3P
QfixV,G 3
(29)
IngestionG 2N =
IngestionG 2P =
and for flagellates the equations were:
g3G3Qfix,BN
QfixV,B
(30)
g3G3Qfix,BP
QfixV,B
(31)
IngestionG 3N =
IngestionG 3P =
4
g1 = % gmax1MIN
k=1
uk − uthk
(SZ :SP )k
kG 1 + uTot
(32)
uk = f1QfixV,f 1, f2QfixV,f 2, f3QfixV,f 3,
(33)
or G2QfixV,G 2
uTot = f1QfixV,f 1 + f2QfixV,f 2 + f3QfixV,f 3
(34)
+ G2QfixV,G 2
(1−x)
IngestionG 1Si =
where Qfix,BN and Qfix,BP were the fixed cellular N
and P content of the bacteria group (mm3 cell − 1),
respectively, and all other symbols were the same
as defined previously.
The prey volume-based growth rate for copepods (mm3 individual − 1 day − 1) was a function of
the volume concentration of all possible prey and
the body size of the copepod relative to the cell
size of the prey group. The equations depicting
copepod growth rate were as follows:
where gmax1 is the maximum grazing rate for
copepods (mm3 individual − 1 day − 1), u k is the
concentration of a specific prey expressed in units
of cellular volume, mm3 l − 1 (where k= 1–4 represented the phytoplankton intermediate group, Pspecialist, N-specialist, and ciliate group,
respectively), uthk is the grazing threshold of a
prey group (mm3 l − 1) as suggested by (Nielsen,
1994), uTot is the sum of all possible prey (mm3
l − 1), kG 1 is the grazing half saturation constant
for copepods (mm3 l − 1), SZ :SP is a value dependent on the ratio between the cell size of the
copepod group and specific prey group (discussed
more below), and all other symbols were the same
as defined previously. A grazing preferencing
scheme based on food quality has been linked to
this Monod relationship (Fasham et al., 1990). In
this model, however, food quality (in this case
amount of N and P in a prey cell) is accounted for
with the zooplankton ingestion equations.
As with the N- and P-ingestion equations, the
prey volume-based growth rate equations (mm3
individual − 1 day − 1) for ciliates and flagellates
were more simplistic because each had only one
source of prey. The equation for ciliates and
flagellates were:
g2 = gmax2
G3QfixV,G 3 − uth,G 3
(SZ :SP )
kG 2 + G3QfixV,G 3
(35)
g3 = gmax3
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
BQfixV,B − uth,B
(SZ :SP )
kG 3 + BQfixV,B
(36)
respectively, where gmax2 and gmax3 are the maximum grazing rate for the ciliate and microzooplankton
groups,
respectively
(mm3
−1
−1
individual
day ), uth,G 3 and uth,B were the
grazing thresholds for the microzooplankton and
bacteria groups, respectively (mm3 l − 1), kG 2 and
kG 3 were the grazing half saturation constant for
the ciliate and microzooplankton groups, respectively (mm3 l − 1), and all other symbols were the
same as defined previously.
Zooplankton have been shown to have an optimal size ratio between grazer and prey were grazing rates are maximized. In addition, there exists a
minimum size ratio below which grazing is no
longer possible, and a maximum size ratio above
which grazing is no longer possible. These values
are based on morphological characteristics of the
zooplankton, such as setae distribution and gape
size, and therefore vary between zooplankton species (Sterner, 1989; Hansen et al., 1994). To represent this process in the model additional functions
specific to each zooplankton group were required,
SZ :SP, which further constrained the zooplankton
group grazing rates. The relationships were based
on a sine function, i.e. had a value between 0 and
1, and fit to data presented elsewhere (Hansen et
al., 1994). To determine the actual growth rate for
a specific zooplankton group, Liebig’s Law of the
Minimum was applied to SZ :SP and the Monod
relationship that described the influence of relative prey availability.
253
4.11. Zooplankton mortality
Mortality to the copepod and ciliate groups
(individuals l − 1 day − 1) was represented using the
same type of equation used previously (Nielsen,
1994; Norberg and DeAngelis, 1997). The equation was:
MortalityGj = mGjGj
(38)
where mGj is a group specific mortality rate
(day − 1). This term was intended to represent
losses to higher trophic levels through feeding
processes. Because microflagellates are too small
for ingestion by most organisms representative of
higher trophic levels, no mortality term was applied. Regarding copepods, because of the diel
vertical migration behavior simulated in the
model, mortality losses to higher trophic levels
only occurred at night.
4.12. Grazing losses to zooplankton by other
zooplankton
The loss to the ciliate group through copepod
grazing, and the loss to the microflagellate group
though ciliate grazing (individuals l − 1 day − 1)
were a function of the predator grazing rate and
concentration, and were expressed with:
GrazingG 2 =
g1G1
QfixV,G 2
(39)
GrazingG 3 =
g2G2
QfixV,G 3
(40)
For the same reasons given for the bacterial
respiration equations, losses from each zooplankton group due to respiration (individuals l − 1
day − 1) were also dependent on growth and
biomass following:
respectively, where all symbols were the same as
previously defined. Because zooplankton cohorts
(or different life stages) were not simulated in this
model, and adult copepods are not known to feed
on other adults, no grazing losses to the copepod
group by other zooplankton was incorporated in
the model.
RespirationGj = r 1GjGrowthGj +r 2GjGj
4.13. Remineralization of N and P by bacteria
4.10. Zooplankton respiration
1
Gj
(37)
where r is the growth dependent respiration for
each zooplankton group (unitless), r 2Gj is the
biomass dependent respiration for each zooplankton group (day − 1), and all other symbols were the
same as defined previously.
For the purposes of this model the N and P
content of the bacteria were constant. In order to
maintain these fixed cellular pools, the loss of N
and P from the bacteria group had to be propor-
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
254
tional to the cell loss. Regarding respiration losses
from the bacteria group (cells l − 1 day − 1), proportional losses of N and P were necessary and were
referred to as N- and P-remineralization (mmol N
l − 1 day − 1, mmol P l − 1 day − 1). The equations for
N- and P-remineralization were determined using:
product from an organism representative of a
higher trophic level. Therefore, the N lost from
zooplankton due to mortality was placed in the N
pool rather than the DON pool.
RemineralizationBN =Qfix,BNRespirationB
(41)
RemineralizationBP =Qfix,BPRespirationB
(42)
The equation describing uptake of N (mmol N
l − 1 day − 1) by phytoplankton and bacteria was a
function of the total N sources available coupled
to bacterial growth, and the uptake rate and
concentration of the phytoplankton groups, and
was described with:
N
UptakefN,BN = GrowthBQfix,BN
N+DON
respectively, where all symbols were the same as
defined previously.
4.14. Excretion of N and P by zooplankton
The N and P content of the varied zooplankton
groups were also constant. In order to maintain
these fixed cellular pools the N and P losses had
to be proportional to the cell losses. To balance
respiration losses (individuals l − 1 day − 1), N and
P excretion terms (mmol N l − 1 day − 1, mmol P l − 1
day − 1) were introduced, using:
3
ExcretionG totalN = % RespirationGiQfix,GiN
3
+ % fi UptakefiN
(47)
i=1
where all symbols were the same as defined
previously.
4.17. Recycling of P and Si, and production of
DON by copepod sloppy feeding
(43)
j=1
3
ExcretionG totalP = % RespirationGjQfix,GjP
4.16. Uptake of N by phytoplankton and bacteria
(44)
j=1
respectively, where all symbols were the same as
defined previously.
The equations describing recycling of P
and production of DON (mmol P l − 1
mmol Si l − 1 day − 1, mmol DON l − 1
through the process of copepod sloppy
were:
and Si,
day − 1,
day − 1)
feeding
SloppyG 1P = xIngestionG 1P
(48)
4.15. Production of N and P due to zooplankton
mortality
SloppyG 1Si = xIngestionG 1Si
(49)
SloppyG 1DON = xIngestionG 1DON
(50)
Similarly, losses due to zooplankton mortality
(individuals l − 1 day − 1) were balanced with proportional losses of N and P (mmol N l − 1 day − 1,
mmol P l − 1 day − 1). For N and P this was
achieved using:
respectively, where all symbols were the same as
defined previously. Because the N produced was
through mastication of prey biomass (sloppy feeding), the liberated N was placed into the DON
pool rather than the N pool.
3
MortalityG totalN = % MortalityGiQfix,GiN
(45)
j=1
4.18. Recycling of P and Si, and production of
DON by zooplankton egestion
3
MortalityG totalP = % MortalityGjQfix,GjP
(46)
j=1
respectively, where all symbols were the same as
defined previously. Because zooplankton mortality was a function of feeding by higher trophic
levels, the N was considered to be an excretion
Because the N and P content of the zooplankton groups were constants, equations describing
removal of excess non-limiting nutrients, referred
to as egestion, were necessary. For example, egestion of N occurred only when a zooplankton
group was P-limited, and egestion of P occurred
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
only when a zooplankton group was N-limited.
All Si ingested was egested. The equations describing egestion of P, Si, and N (mmol P l − 1
day − 1, mmol Si l − 1 day − 1, mmol DON l − 1
day − 1) were:
3
EgestionG totalP = % IngestionGjP
j=1
−IngestionGjN
Qfix,GjP
Qfix,GjN
EgestionG 1Si =IngestionG 1Si(1 − x)
(51)
3
j=1
−IngestionGjP
Qfix,GjN
Qfix,GjP
Losses of N, P and Si from the phytoplankton
groups relating to respiration (cells l − 1) were
made a function of the N, P, and Si content at the
time of respiration, referred to now as exudation.
For exudation of P, Si, and N (mmol P l − 1 day − 1,
mmol Si l − 1 day − 1, mmol DON l − 1 day − 1) the
equations were:
Exudationf totalP = % RespirationfiQfiP
(57)
Exudationf 1Si = Respirationf 1Qfix,f 1Si
(58)
i=1
3
Exudationf totalDON = % RespirationfiQfiN
(59)
i=1
(53)
respectively, where all symbols were the same as
defined previously. Because ingested N was previously a component of the prey biomass, egested N
was placed into the DON pool rather than the N
pool.
4.19. Recycling of P and Si, and production of
DON through phytoplankton mortality
Losses of N, P and Si from the phytoplankton
groups relating to mortality (cells l − 1) were made
a function of the N, P, and Si content at the time
of mortality. For mortality based P, Si, and N
production (mmol P l − 1 day − 1, mmol Si l − 1
day − 1, mmol DON l − 1 day − 1) the equations
were:
3
Mortalityf totalP = % MortalityfiQfiP
(54)
Mortalityf 1Si =Mortalityf 1Qfix,f 1Si
(55)
i=1
3
Mortalityf totalDON = % MortalityfiQfiN
4.20. Recycling of P and Si, and production of
DON through phytoplankton exudation
3
(52 c )
EgestionG totalDON = % IngestionGjN
255
(56)
i=1
respectively, where all symbols were the same as
defined previously. Because the N produced
though phytoplankton mortality was previously
incorporated in phytoplankton biomass, it was
placed into the DON pool rather than the N pool.
respectively, where all symbols were the same as
defined previously. Again, because the N produced though phytoplankton exudation is from
phytoplankton biomass, it was placed into the
DON pool rather than the N pool.
4.21. Uptake of P by phytoplankton and bacteria
The equation describing uptake of P (mmol P
l − 1 day − 1) by phytoplankton and bacteria was a
function of the bacterial growth and the uptake
rate and concentration of the phytoplankton
groups, and was described with:
3
UptakefP,BP = GrowthBQfix,BP + % fi Uptakefi
i=1
(60)
where all symbols were the same as defined
previously.
4.22. Uptake of Si by phytoplankton
(intermediate group only)
The equation describing uptake of Si (mmol Si
l − 1 day − 1) by the intermediate group was a function of the growth of the intermediate group, and
was expressed with:
Uptakef 1Si = Growthf 1Qfix,f 1Si
(61)
where all symbols were the same as defined
previously.
256
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
4.23. Uptake of DON by Bacteria
The equation describing uptake of DON (mmol
DON l − 1 day − 1) by bacteria was made a function of the total N sources available and the
bacterial growth, and was described using:
UptakeBDON =GrowthBQfix,BN
DON
N + DON
(62)
where all symbols were the same as defined
previously.
4.24. Ad6ection inputs and losses
As in a previous study (Nielsen, 1994) advection inputs and losses for each pool represented in
the model (N, P, Si, DON, fi, Gj, and B) were a
function of the specific flow rate (inflow divided
by ecosystem volume), the concentration of a
specific constituent in the input source, and the
concentration of a specific constituent in the simulation, and was depicted using:
Advection=nCsource −nCx
(63)
where n is the specific flow rate (day − 1), Csource is
the concentration of a specific constituent in the
input source (mmol l − 1), and Cx is the concentration of a specific constituent in the simulation.
5. Model validation and evaluation
5.1. Explanation of tests
To reiterate a point stated previously, the intent
of this paper was to generate a tool to be used to
elucidate potential algal bloom mechanisms and
determine sensitivity of such mechanisms to various abiotic and biotic processes. It was not the
intent of this research to produce a predictive
model. Nevertheless validation and evaluation of
the model is necessary. The behavior of the model
was tested in two ways. First, the ability of the
model to predict accumulation of phytoplankton,
bacteria, and microflagellate biomass was tested
by comparing simulation results with data from
the sewage-impacted NRE at a time when the
initial conditions prior to a major disturbance
could be estimated, and the nature of the disturbance and the period of phytoplankton growth
after the disturbance were well understood. Unfortunately, the data did not contain information
regarding copepod and ciliate distributions. In a
previous study the equations of the model depicting phytoplankton dynamics, i.e. phytoplankton
growth rate, accumulation of biomass, nutrient
uptake rate, and cellular storage of N and P were
validated (Roelke et al., 1999). The second test
related to the behavior of the model where interactions between the various pools were the focus.
It was not the intent of the second test to simulate
a seasonal shift that would occur in a natural
environment. To do this, processes such as temperature variation, water column stability, and
depth of mixing would need to be incorporated,
which was not the case or purpose here.
5.2. Model 6alidation test and results (in addition
to Roelke et al., 1999)
For the first test, the model was compared to
data reported from NRE for August 1994
(Roelke, 1997; Roelke et al., 1997). The NRE had
experienced a prolonged period of no flow from
the Nueces River but continual input from a
sewage treatment plant, which was followed by a
large pulse that resulted in an 4-day hydraulic
residence time for NRE. Using data from a station adjacent to the Nueces River input to initialize the model, and using knowledge of the Nueces
River flow and nutrient concentration, as well as
knowledge of the nutrient loading from the
sewage treatment plant, a 4-day simulation was
conducted. The values used to initialize the model
are reported in Appendix A. Regarding the nutrient loading from the sewage treatment plant, historical records showed the nutrient concentrations
for N and P were highly variable over periods as
short as days, while the volume of discharge was
remarkably consistent (Roelke, 1997). Therefore,
for this model test the N and P concentration of
the sewage treatment plant discharge was adjusted, within the range of reported values, to fit
the measured concentration of N and P in NRE
(Roelke et al., 1997) given the known hydrology.
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
257
Fig. 2. Comparison of the first simulation test to field data collected in the Nueces River estuary. For the field data, the initial
conditions prior to a major disturbance were estimated, and the nature of the disturbance and the period of phytoplankton growth
after the disturbance were well understood. These were used to initialize the model simulation. Data were not available for copepod
and ciliate abundance comparisons.
After a 20% increase in the bacterial half-saturation coefficients for N and P uptake, and a
4-fold increase in the derived half-saturation coefficient for ciliate grazing on microflagellates (see
Appendix A), the model simulation results were
very similar to measured values for the August
NRE data (Fig. 2). An 30% overestimation of
phytoplankton accumulated biomass was not surprising because the parameters depicting the phytoplankton groups were not ‘tweaked’ to optimize
the model’s performance. Rather the phytoplankton groups built into the model were based on
species for which there was available information
on nutrient uptake and growth kinetics, which
were not the same species present in NRE during
August 1994. In addition, parameterization of
these phytoplankton groups were identical to a
previous study (Roelke et al., 1999), which allowed a direct comparison between studies (highlighted later).
5.3. Model beha6ior test and results
For the second simulation test the initial conditions and nutrient loading were the same as the
previous test, only the model simulation was for a
longer period. Again, the purpose for the second
test was to evaluate the behavior of the model
where interactions between the various pools were
the focus, not to predict seasonal cycles.
Results from this test showed the Lotka–
Volterra type behavior of the model. In this simulation phytoplankton accumulated biomass was
grazed away, followed by a peak in copepod
concentration and subsequent crash after all prey
sources were exhausted, and a repeat of the cycle
(Fig. 3a–c). The microbial loop showed consecutive population peaks in bacteria, flagellates, and
ciliates, with the demise of each population
mostly due to grazing pressure (Fig. 3c–e). Phytoplankton growth and accumulation of biomass
were predominately controlled through copepod
grazing, and nutrients were non-limiting (Fig. 3f,
g, i, j). This explains why competitive exclusion
among the phytoplankton groups was not evident, even though the N:P loading ratio favored
the N-specialist (Fig. 3h). Results from this simulation test were reasonable with reported values
from NRE, where accumulated algal biomass
ranged from 0.01 to 1.4× 108 mm3 l − 1, bacteria
concentrations from 0.3 to 7.3× 109 cells l − 1,
flagellates from 0 to 0.2×108 cells l − 1, N
concentrations from 0 to 35 mM, and P concentrations 0.5 to 14 mM (Roelke et al., 1997).
258
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
6. Model use
6.1. Rationale behind simulations used to
in6estigate plankton succession
Model simulations were conducted with the
intent to explore synergistic processes effecting
phytoplankton succession, accumulation of algal
biomass, and secondary productivity, and then to
determine the sensitivity of these processes to
various abiotic conditions. Because the emphasis
of this research was on multiple limiting nutrients,
simulations were conducted where nutrients actually became limiting. To achieve this, the nutrient
Fig. 3. The second simulation test showed the Lotka–Volterra type behavior of the model when nutrient loading conditions were
high. The phytoplankton groups were controlled through copepod grazing activity and no competitive exclusion processes were
apparent despite the very low N:P of the nutrient loading.
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
loading and volume inputs were decreased from
the values used for the validation and evaluation
tests described above (this was done by removing
the influence of the sewage treatment plant from
the model runs). To better investigate how the
mentioned processes influenced phytoplankton
succession, the phosphorus loading was adjusted
to produce nutrient loading ratios of either 10.5
or 20.5. In a previous study it was shown that
these ratios corresponded to the optimal nutrient
ratios for the N- and P-specialist, respectively,
and that when nutrients were loaded at either
optimal ratio these algae were able to out-perform
their competitors as conditions approached steady
state (Roelke et al., 1999). Because the simulations described below have no resemblance to
conditions in the NRE, results should not be
extrapolated to existing data for this ecosystem.
Again, I reiterate that the intent of the simulations was to elucidate potential algal bloom mechanisms and determine sensitivity of such
mechanisms to various abiotic and biotic processes, not to predict succession events in NRE.
6.2. Details of four simulations with 6aried abiotic
conditions
The first simulation received an N input where
the concentration of the source water was 0.7 mM,
which was the August value for the NRE data
(Roelke et al., 1997). The phosphorus concentration was adjusted to produce an N:P loading of
10.5. All other initial conditions for this simulation are listed in Table 3. The model run was for
a 120-day period and the loading was continuous.
This simulation was used as the standard case,
and is referred to as the bloom scenario for
reasons that will become obvious.
The second simulation differed from the first
only in that the N and P concentrations in the
source water were slightly increased, i.e. N
changed from 0.7 to 1.0 mM N and P changed
from 0.067 to 0.095 mM P. Because this was the
only difference, this simulation was referred to as
the magnitude change scenario.
The third simulation differed only from the first
in that the mode in which the nutrients were
delivered was changed. For this simulation the
259
river flow was pulsed once every three days, the
other two days no flow occurred. On days of a
pulse the flow was three times greater than the
bloom scenario, while the N and P concentrations
were the same. Because this was the only difference, this simulation was referred to as the mode
change scenario.
The final simulation differed only from the first
in that the P concentration in the source water
was approximately halved. Previous simulations
showed that the N-content of the phytoplankton
was controlling copepod growth. Because of this,
N-loading was held constant and the concentration of P was adjusted. This resulted in a shift
away from the optimal ratio of the N-specialist
(10.5) towards the P-specialist (20.5), while copepod growth remained N-limited. Because this was
the only difference, this simulation was referred to
as the ratio change scenario.
6.3. Comparison between simulations results
Surprisingly, during the first simulation a
bloom of the N-specialist resulted and secondary
productivity ceased (Fig. 4a). Recall that no direct
bloom-forming mechanisms, e.g. grazing inhibition, were ‘forced’ in the model simulations. To
elucidate the underlying mechanism causing this
bloom, comparisons were made with the second
simulation, the magnitude change scenario, were
loading of nutrients were slightly greater (Fig. 4b).
The timing of the onset of bottom–up control
(nutrient limitation) in relation to the timing of
the onset of top–down control (grazing) of phytoplankton dictated whether a bloom of the N-specialist would occur. During the magnitude change
scenario all three phytoplankton species grew
more quickly than during the bloom scenario,
because both N and P were added at greater
concentrations. Early in this simulation, however,
more rapid phytoplankton growth did not translate to more accumulated phytoplankton biomass.
In fact, up to day 30 accumulated phytoplankton
biomass was very similar between the bloom and
magnitude change scenarios. This was due to the
increased grazing pressure and accumulation of
copepod biomass during the magnitude change
scenario (Fig. 4a, b). Copepods accumulated
260
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
Fig. 4. The model behavior when nutrient loading was reduced to a level where nutrients could become limiting. The bloom case
scenario (A) resulted in exclusion of two phytoplankton groups and cessation of secondary productivity. The other three scenarios
represented varied abiotic conditions of the model that were different from the bloom case scenario. Variations were a magnitude
change (B) in nutrients loaded, i.e. increased N and P, a change in the mode of loading from continuous to pulsed (C), and a change
in the ratio of nutrients loaded, i.e. decreased P (D). All changes resulted in increased phytoplankton species diversity, enhanced
secondary productivity, and prevention of the algal bloom.
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
biomass during the bloom scenario as well, but at
a slower rate (Fig. 4a). Because of this, the bulk
of the copepod grazing activity during this simulation coincided with the period when the phytoplankton were in a ‘starved’ condition, i.e. the
cell-quota for N and P was near the value of the
critical cell-quota (Fig. 4a).
As noted previously, grazers were depicted as
selective feeders based on individual prey concentration, prey availability relative to all potential
prey, and the size of the prey relative to the
predator. Grazing rate was not a function of the
‘quality’ of the prey. The critical cell-quota regarding N for P. minimum, on which the N-specialist was based, is very low (see Appendix A).
Under the conditions of the bloom scenario, the
N-content of the N-specialist in a ‘starved’ condition was too low to support enough copepod
growth to offset total copepod losses, which included respiration processes, mortality, and advection. This was not true for the intermediate
group and P-specialist. Therefore, after the intermediate group and P-specialist were out-competed
and depleted through advection and grazing
losses, the copepods simply were flushed out of
the system. In the absence of a predator the
N-specialist bloomed.
The third simulation, the mode change scenario, also prevented a bloom of the N-specialist.
For this scenario two controlling processes were
elucidated that prevented the algal bloom. The
first process related to the ability of the phytoplankton groups to uptake and store nutrients at
a rate greater than their reproductive growth rate.
This resulted in brief periods, which coincided
with the nutrient pulses, were the N and P cellquotas for the phytoplankton groups were elevated (Roelke et al., 1999). This prevented the
N-specialist from remaining in a starved state, i.e.
below the copepod food-quality threshold.
The second process that prevented the algal
bloom was the diel migratory nature of the copepod group, i.e. copepods were present at the
surface and subject to advection losses only during the night. During the day copepods did not
feed at the surface and were not subject to advection losses. The mode change scenario was set up
to deliver a pulse according to a sine function.
261
This meant that the minimum hydraulic residence
time, or the time of maximum advection losses,
was at 12:00 noon when the copepods were not in
surface waters.
A combination of the brief periods of enhanced
N cell-quota under pulsed conditions and the
simulated diel vertical migration of the copepod
group lead to greater growth and accumulation of
copepod biomass. Again, the controlling mechanism that determined whether a bloom would
occur was the timing of the onset of bottom–up
and top–down control of the phytoplankton.
During the mode change scenario grazing depleted the phytoplankton before the N-specialist
reached a ‘starved’ condition, i.e. all phytoplankton contained an amount of intracellular-N great
enough to support copepod growth and offset
total copepod losses (Fig. 4c).
The ratio change scenario, as with the magnitude and mode change scenarios, also prevented
the bloom of the N-specialist. For this scenario,
the underlying process that prevented the algal
bloom was the ability of phytoplankton species to
sequester non-limiting nutrients that would eventually limit growth of competing algae. As was the
case for all three comparative simulations, the
N-specialist was P-limited early in the simulation,
whereas the other two algae were N-limited (Fig.
4a–d). Reducing the amount of P-loading caused
the N-specialist to grow slower (Fig. 4d). This
resulted in the N-specialist sequestering less N, i.e.
making more N available for growth of the other
phytoplankton groups. As stated previously, the
intermediate group and P-specialist were suitable
food sources for the copepods regardless of their
nutritional status. The net result of the ratio
change (less P) was greater growth and accumulation of copepod biomass (Fig. 4d). As before, the
controlling mechanism was that the onset of topdown control occurred before the N-specialist
reached a starved condition, which in turn prevented an algal bloom.
7. Discussion
Critical to the findings of this study is the
existence of a food-quality threshold below which
262
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
a predator can no longer survive, regardless of
the prey density. Do such thresholds exist for
predators in natural environments? There is a
vast body of literature demonstrating that foodquality in terms of N- and P-content directly
impact population dynamics of grazers, i.e.
predator growth, reproductive success, and accumulation of biomass are positively correlated to
the N- or P-content of the prey. This was suggested as a controlling process in some natural
environments (Gleitz et al., 1996; Savage and
Knott, 1998) and mesocosm studies (Prins et al.,
1995), and shown to occur in laboratory experiments (Sommer, 1992; Sterner et al., 1993;
Lurling and Donk, 1997). These studies did not
show that feeding on prey of poor food-quality
resulted in the demise of a predator population,
i.e. not just poorer performance but elimination,
which is what the results of this study, and another modeling study (Hessen and Bjerkeng,
1997), suggest. This concept deviates from classical predator-prey theory, and has yet to be
demonstrated in a natural environment. Some
laboratory experiments, on the other hand, support this concept. For example, in one study it
was shown that a single predator failed to grow
when offered only one prey source of poor
food-quality (Sommer, 1992). In another experiment, a natural phytoplankton assemblage
bloomed and secondary grazers died off under
conditions of continuous loading, i.e. approaching steady state, while under conditions of
pulsed nutrient supply the same phytoplankton
assemblage remained cropped and secondary
consumer populations grew and were sustained
(Roelke and Buyukates, 1999).
In theory, the existence of food-quality
thresholds for predators in natural environments
seems logical. Its role as a process influencing
plankton succession, however, may vary with
plankton species diversity and the dynamic nature of the aquatic environment. For example,
when many prey selections are available there is
a chance that one of the coexisting species will
not be below the food-quality threshold, even
when starved. In this case, the excess nutrient
content from this one species may result in a
prey community whose total nutrient content is
above the food-quality threshold, even though
other members of the community may be below
the threshold. Similarly, communities that are
characteristic of many grazers are likely to have
members with varying food-quality thresholds.
As long as the food-quality threshold remains
above the threshold of the grazer with the least
nutrient requirement, grazing will continue and
ambient nutrients will be made available. In
turn, this may replenish the nutrient content of
the starved prey (Prins et al., 1998, but see Elser
and Urabe, 1999) and allow all grazers to persist. Finally, predator food-quality thresholds
are not constants. Because they are a function
of the nutrient content of the prey relative to
loss mechanisms, such as respiration, mortality,
and advection, they will vary with each of these
processes. For example, model simulations not
reported here showed that the copepods were
able to thrive under conditions of no flow while
feeding on starved algal cells that under conditions of flow were unacceptable. This argument
highlights the importance of both species diversity and fluctuating environments. Processes that
reduce diversity, such as introduction of pollutants or exotic species, or reduce the dynamic
nature of an ecosystem, such as water diversion
projects and construction of reservoirs, may ultimately increase the vulnerability of an ecosystem
to algal blooms where poor food-quality is the
bloom-initiating process.
The influence of food-quality thresholds on
plankton succession is likely to be coupled to
other important processes (see Sommer, 1989a,b;
Anderson and Garrison, 1997). In the present
study, however, the predator food-quality
threshold was the most important feature of the
model. These findings may have implications regarding the way we manage point source nutrient inputs to aquatic environments. For
example, the timing of the onset of bottom–up
and top–down control of phytoplankton, the
underlying mechanism controlling whether a
bloom would ensue, was sensitive to abiotic
conditions that are possible to manipulate, i.e.
magnitude, mode, and ratio of nutrient loading.
To further test the concepts presented here in a
management context, in-field and mesocosm ex-
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
periments are necessary to better explore synergistic interactions between predator food-quality
thresholds and other processes that impact plankton community dynamics.
263
nutrient loading it was possible to maintain phytoplankton species diversity, enhance secondary productivity, and prevent an algal bloom.
Acknowledgements
8. Summary
The model simulations illustrated the potential
importance of food-quality thresholds for predators
as they influence phytoplankton succession, accumulation of algal biomass, and secondary productivity. In the extreme, these findings indicate that
secondary productivity can collapse and a bloom
result when phytoplankton are of poor food-quality, regardless of their concentration. This finding
deviates from classic predator – prey models. The
mechanism controlling whether an algal bloom
would occur was the timing of the onset of bottom –
up control relative to the onset of top – down
control. When top down control occurred prior to
bottom–up control, prey were of acceptable quality, copepod growth and accumulation of biomass
followed, and classical Lotka – Volterra behavior
ensued. On the other hand, when bottom – up
control occurred before top – down control, some
prey were of poor quality, secondary productivity
ceased, and an algal bloom occurred. The timing
of the onset of bottom – up and top – down control
was highly sensitive to some abiotic conditions. By
manipulating the magnitude, mode, and ratio of
The author is grateful to reviewers for their
insightful comments on a previous version of this
manuscript. A portion of this research was performed while the author held a CORE/NRL Postdoctoral Fellowship.
Appendix A
The appendix is divided into two sections. The
first section lists the constant parameters of the
model with reference to citations from which the
information was obtained. The section lists the
variable parameters of the model as well as the
input sources, initial values of the appropiate
parameters are listed as well. Throughout the
appendix the letters i and j are used in subscript
notation. The letter i refers to the phytoplankton
groups. It has a value between 1 and 3, where
1= intermediate group, 2= P-specialist, and 3=
N-specialist. The letter j refers to the zooplankton
groups and also has a value between 1 and 3,
where 1= copepod group, 2= ciliate group, and
3= microflagellate group.
A.1. Model constants
Symbol
Description
Units
i, j= 1
i, j= 2
i, j= 3
Reference
and/or notes
afiN
Phytoplankton group
P-uptake
factor when
N-limited
–
0.01
0.01
0.01
Roelke et
al., 1999
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
264
Bacteria
cell size,
equivalent
spherical
diameter
Zooplankton
cell size,
equivalent
spherical
diameter
mm
0.80
mm
200
30
3
Phytoplankton cell size,
equivalent
spherical
diameter
Bacterial
half saturation coefficient for Nand DONdependent
growth
Bacterial
half saturation coefficient for
P-dependent
growth
mm
12.4
8.14
10.2
mmol N/DON l−1
0.78
mmol P l−1
0.078
kGj
Zooplank
ton group
half saturation coefficient for
grazing rate
mm3 l−1
1.12×109
2.11×109
3.18×109
kfiN
Phytoplankton group
half saturation coefficient for N
uptake
Phytoplankton group
half saturation coefficient for P
uptake
mmol N l−1
0.820
1.00
0.300
mmol P l−1
0.065
0.100
1.00
ESDB
ESDGj
ESDfi
kBN
kBP
kfiP
Roelke, 1997;
Roelke et al.,
1997
Selected
within reported values
from Hansen
et al., 1994;
Dagg, 1995;
Roelke, 1997
Bold and
Wynne, 1985;
Tomas, 1996
Adjusted up
from
Fuhrman et
al., 1988;
Gude, 1989;
Suttle et al.,
1990
Adjusted up
from
Fuhrman et
al., 1988;
Gude, 1989;
Suttle et al.,
1990
Derived and
adjusted from
Redfield et
al., 1963;
Evans and
Parslow,
1985; Fasham
et al., 1990
Roelke et al.,
1999
Roelke et al.,
1999
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
kf 1Si
mGj
mfi
Qfix,BN
Qfix,BP
Intermediate group
half saturation coefficient for
Si-dependent
growth
Zooplankton group
specific mortality rate
Phytoplankton group
specific mortality rate
Bacteria
cellular composition of
N
265
mmol Si l−1
3.0
–
–
Derived from
Dortch and
Whitedge,
1992; Dortch
et al., 1994
day−1
0.10
0.10
–
day−1
0.09
0.09
0.09
Assumed as a
feeding loss
from higher
trophic level
Fasham et al.,
1990
mmol N cell−1
2.79×10−9
Bacteria
mmol P cell−1
cellular composition of
P
0.260×10−9
Qfix,GjN Zooplankmmol N individual−1 4.40×10−3
ton group
cellular composition of
N
2.50×10−5
2.67×10−8
Derived from
Fuhrman,
1992; Lee and
Fuhrman,
1987; Roelke,
1997; Roelke
et al., 1997
Derived from
Fuhrman,
1992; Lee and
Fuhrman,
1987; Roelke,
1997; Roelke
et al., 1997
Derived using
Redfield et
al., 1963;
Bernard and
Rassoulzadegan, 1993;
Hansen et al.,
1994; Sterner
and Hessen,
1994; Dagg,
1995; Simek
et al., 1995
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
266
Qfix,GjP
Zooplankmmol P individual−1 0.147×10−3 0.156×10−5 0.167×10−8
ton group
cellular composition of
P
QfixV,B
Bacteria
cellular volume
Zooplankton group
cellular volume
mm3 cell−1
0.268
mm3 cell−1
4.19×106
1.41×104
14.1
Phytoplankton group
cellular volume
Phytoplankton intermediate group
cellular composition of
Si
Phytoplankton group
maximum N
cell-quota
Phytoplankton group
maximum P
cell-quota
Phytoplankton group
minimum N
cell-quota
Phytoplankton group
minimum P
cell-quota
mm3 cell−1
998
282
556
mmol Si cell−1
767×10−9
–
–
mmol-N cell−1
767×10−9
180×10−9
119×10−9
mmol P cell−1
89.0×10−9 17.0×10−9 23.2×10−9 Roelke et al.,
1999
mmol N cell−1
110×10−9
mmol P cell−1
6.85×10−9 1.43×10−9 1.95×10−9 Roelke et al.,
1999
QfixV,Gj
QfixV,fi
Qfix,f 1Si
Qmax,fiN
Qmax,fiP
Qmin,fiN
Qmin,fiP
Derived using
Redfield et
al., 1963;
Bernard and
Rassoulzadegan, 1993;
Hansen et al.,
1994; Sterner
and Hessen,
1994; Dagg,
1995; Simek
et al., 1995
Roelke, 1997;
Roelke et al.,
1997
Selected
within reported values
from Hansen
et al., 1994;
Dagg, 1995;
Roelke, 1997
Bold and
Wynne, 1985;
Tomas, 1996
Derived from
Brzezinski,
1985;
Levasseur and
Therriault,
1987
Roelke et al.,
1999
30.8×10−9 20.4×10−9 Roelke et al.,
1999
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
r 1B
r 2B
r 1Gj
r 2Gj
rfi
SZ1:SP
SZ :SP
Vmax,fi
Bacteria
growthdependent
respiration
factor
Bacteria
biomassdependent
respiration
factor
Zooplankton group
growthdependent
respiration
factor
Zooplankton group
biomassdependent
respiration
factor
Phytoplankton group
respiration
factor
Copepod
optimal
pred:prey
function for
phytoplankton groups
Pred:prey
function for
Copepods:
Ciliate,
Ciliate:
Flagellate,
Flagellate:
Bacteria
Phytoplankton group
maximum
light-dependent specific
growth rate
267
–
0.4
Derived from
Riley et al.,
1949; Jahnke
and, Craven
1995
Derived from
Riley et al.,
1949; Jahnke
and Craven,
1995
Derived from
Riley et al.,
1949; Checkley, 1980;
Dagg et al.,
1991
Derived from
Riley et al.,
1949; Checkley, 1980;
Dagg et al.,
1991
Geider, 1992
day−1
0.12
–
0.50
0.50
0.50
day−1
0.12
0.12
0.12
–
0.17
0.17
0.17
–
0.97
0.95
1.0
Derived from
Sterner, 1989;
Hansen et al.,
1994
–
0.20
0.99
0.99
Derived from
Sterner, 1989;
Hansen et al.,
1994
day−1
2.20
2.20
2.20
Parsons et al.,
1984
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
268
afi
gmaxj
mmax,B
m̄max,fiN
m̄max,fiP
mmax,f 1Si
rmax,fiN
Phytoplank- cm2 s quanta−1 day−1 5.3×10−18
ton group
slope of the
photosynthesis–irradiance curve
Zooplankmm3 individual−1 day−1 9.45×107
ton group
maximum
growth rate
in terms of
volume of
prey
Bacterial
maximum
specific
growth rate
Phytoplankton group
N-limited
maximum
specific
growth rate
Phytoplankton group
P-limited
maximum
specificgrowth
rate
Intermediate group
Si-limited
maximum
specific
growth rate
Phytoplankton group
N-uptake
rate measured at m̃
5.3×10−18 5.3×10−18 Parsons et al.,
1984
2.98×104
14.3
Derived from
Smayda,
1978; Verity,
1985; McManus and
Fuhrman,
1988; Dagg et
al., 1991;
Hansen et al.,
1994; Simek
et al., 1995;
Roelke, 1997;
Roelke et al.,
1997
Ducklow and
Carlson, 1992
day−1
1
day−1
1.60
2.01
1.5
Roelke et al.,
1999
day−1
1.60
1.92
1.50
Roelke et al.,
1999
day−1
1.60
–
–
Assumed
equal to
m̄max,fiN
mmol N cell−1 day−1
1140×10−9 300×10−9 750×10−9 Roelke et al.,
1999
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
rmax,fiP Phytoplank- mmol P cell−1 day−1
ton group
P-uptake
rate measured at m̃
uth
Prey graz- mm3 l−1
ing threshold expressed in
units of cellular volume
x
Copepod
–
sloppy feeding coefficient
269
71.6×10−9
27.0×10−9
71.4×10−9
Roelke et al.,
1999
1.67×104
1.67×104
1.67×104
Selected as
1% of initial
value
0.25
Derived from
Fasham et al.,
1990
A.2. Model 6ariables and input sources: initial parameter 6alues (where appropriate)
Symbol
Description
Units
Afi
Light-dependant
growth factor for
phytoplankton
groups
Bacteria concentration
General constituent concentration for the
input source
General constituent concentration in the
box model
Ambient labile
dissolved organic
nitrogen concentration
Ambient labile
dissolved organic
nitrogen concentration in river
source
–
B
Csource
Cx
DON
DONriver
4 day test
Bloom Magnit
case
change
Mode
change
Ratio
change
1×109
s
s
s
s
mmol DON l−1
0
s
s
s
s
mmol DON l−1
0
s
s
s
s
cells l−1
mass l−1
mass l−1
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
270
DONstp
G1
G2
G3
I
N
Nriver
Nstp
P
Priver
Pstp
Qf 1N
Qf 2N
Qf 3N
Qf 1P
Qf 2P
Qf 3P
Ambient labile
dissolved organic nitrogen
concentration
in stp source
Copepod concentration
Ciliate concentration
Microflagellate
concentration
Irradiance
Ambient nitrogen
concentration
Ambient nitrogen
concentration
in river source
Ambient nitrogen
concentration
in stp source
Ambient phosphorus concentration
Ambient phosphorus concentration in river
source
Ambient phosphorus concentration in stp
source
Intermediate
group N cellquota
P-specialist group
N cell-quota
N-specialist
group N cellquota
Intermediate
group P cellquota
P-specialist group
P cell-quota
N-specialist
group P cellquota
mmol DON l−1
0
individuals l−1
1
s
s
s
s
individuals l−1
1
s
s
s
s
individuals l−1
4.85×103
s
s
s
s
quanta cm−2 s−1
mmol N l−1
0.7
0.7
1.0
0.7
0.7
mmol N l−1
0.7
0.7
1.0
0.7
0.7
mmol N l−1
230
mmol P l−1
3.5
0.067
0.095
0.067
0.034
mmol P l−1
3.5
0.067
0.095
0.067
0.034
mmol P l−1
34
mmol N cell−1
219×10−9
s
s
s
s
mmol N cell−1
61.6×10−9
s
s
s
s
mmol N cell−1
40.9×10−9
s
s
s
s
mmol P cell−1
13.7×10−9
s
s
s
s
mmol P cell−1
2.86×10−9
s
s
s
s
mmol P cell−1
3.90×10−9
s
s
s
s
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
Si
Siriver
Sistp
Vfi
gj
mB
mBN
mBP
mfi
mfiN
mfiP
mf 1Si
n
f1
f2
Ambient Silica
concentration
Ambient Silica
concentration
in river source
Ambient Silica
concentration
in stp source
Light-dependent
specific growth
rate for the
phytoplankton
groups
Growth rate in
terms of volume of prey
for zooplankton groups
Bacteria specific
growth rate
Bacteria N-limited specific
growth rate
Bacteria P-limited specific
growth rate
Phytoplankton
group specific
growth rate
Phytoplankton
group N-limited specific
growth rate
Phytoplankton
group P-limited specific
growth rate
Intermediate
group Si-limited specific
growth rate
Specific flow rate
Intermediate
group cell concentration
P-specialist group
cell concentration
271
mmol Si l−1
10
s
s
s
s
mmol Si l−1
10
s
s
s
s
mmol Si l−1
10
d−1
mm3 individual−1
day−1
day−1
day−1
day−1
day−1
day−1
day−1
day−1
day−1
cells l−1
0.137
1.67×103
0.1
s
0.1
s
0–0.3
s
0.1
s
cells l−1
5.91×103
s
s
s
s
272
f3
u
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
N-specialist
cells l−1
group cell concentration
Prey concentramm3 l−1
tion expressed
in units of cellular volume
References
Anderson, D., Garrison, D. (Eds.), 1997. The Ecology and
Oceanography of Harmful Algal Blooms. Limnology and
Oceanography Special Issue, 42:5:2, American Society of
Limnology and Oceanography.
Bernard, C., Rassoulzadegan, F., 1993. The role of picoplankton (cyanobacteria and plastic picoflagellates) in
the diet of tintinnids. J. Plankton Res. 15, 361–373.
Bold, H.C., Wynne, M.J., 1985. Introduction to the Algae
Structure and Reproduction, Prentice-Hall, Englewood
Cliffs, NJ, 720 p.
Breitburg, D., Seitzinger, S., Sanders, J. (Eds.), 1999. The
Effects of Multiple Stressors on Freshwater and Marine
Ecosystems. Limnology and Oceanography Special Issue,
44:3:2, American Society of Limnology and Oceanography.
Brock, T.D., 1981. Calculating solar radiation for ecological
studies. Ecol. Model. 14, 1–19.
Brzezinski, M.A., 1985. The Si:C:N ratio of marine diatoms:
interspecific variability and the effect of some environmental variables. J. Phycol. 21, 347–357.
Buskey, E., 1993. Annual pattern of micro- and mesozooplankton abundance and biomass in a subtropical
estuary. J. Plankton Res. 15, 907–924.
Checkley, D.M., 1980. The egg production of a marine
planktonic copepod in relation to its food supply: laboratory studies. Limnol. Oceanogr. 25, 430–446.
Dagg, M.J., 1995. Ingestion of phytoplankton by the microand mesozooplankton communities in a productive subtropical estuary. J. Plankton Res. 17, 845–857.
Dagg, M.J., Grimes, C., Lohrenz, S., McKee, B., Twilley,
R., Wiseman, W.W. Jr., 1991. Continental shelf food
chains of the Northern Gulf of Mexico. In: Sherman, K.,
Alexander, L.M., Gold, B.D. (Eds.), Food Chain Yields.
Models and Management of Large Marine Ecosystems.
Western Press, Boulder, CO, pp. 1–40.
DeBaar, H.J.W., 1994. von Liebig’s Law of the Minimum
and plankton ecology. Prog. Oceanogr. 33, 347–386.
DeManche, J.M., Curl, J.H.C., Lundy, D.W., Donaghay,
P.L., 1979. The rapid response of the marine diatom
Skeletonema costatum to changes in external and internal
nutrient concentration. Mar. Biol. 53, 323–333.
Donk, E.V., 1989. The role of fungal parasites in phytoplankton succession. In: Sommer, U. (Ed.), Plankton
Ecology. Springer – Verlag, Berlin, pp. 171–194.
3.00×103
s
s
s
s
Dortch, Q., Whitedge, T.E., 1992. Does nitrogen or silica
limit phytoplankton production in the Mississippi River
plume and nearby regions? Continental Shelf Res. 12,
1293 – 1309.
Dortch, Q., Nelson, D.M., Turner, R.E., Rabalais, N.N.,
1994. Silicate limitation on the Louisiana continental
shelf. Nutrient-Enhanced Coastal Ocean Productivity
Proceedings of the 1994 Synthesis Workshop, NOAA,
Baton Rouge, Louisiana, USA, pp. 34 – 39.
Droop, M.R., 1973. Some thoughts on nutrient limitation in
algae. J. Phycol. 9, 264 – 272.
Droop, M.R., 1983. 25 years of algal growth kinetics: a
personal view. Bot. Mar. 26, 99 – 112.
Ducklow, H.W., Carlson, C.A., 1992. Oceanic bacterial production. In: Marshall, K.C. (Ed.), Advances in Microbial
Ecology, vol. 12. Plenum Press, New York, pp. 113 – 181.
Ebenhoh, W., 1988. Coexistence of an unlimited number of
algal species in a model system. Theor. Popul. Biol. 34,
130 – 144.
Elrifi, I.R., Turpin, D.H., 1985. Steady-state luxury consumption and the concept of optimum nutrient ratios: a
study with phosphate and nitrate limited Selenastrum
minutum (Chlorophyta). J. Phycol. 21, 592 – 602.
Elser, J.J., Urabe, J., 1999. The stoichiometry of consumerdriven nutrient recycling: theory, observations, and consequences. Ecology 80, 735 – 751.
Evans, G.T., Parslow, J.S., 1985. A model of annual plankton cycles. Biol. Oceanogr. 3: 327 – 347.
Fasham, M.J.R., Ducklow, H.W., McKelvie, S.M., 1990. A
nitrogen based model of plankton dynamics in the
oceanic mixed layer. J. Mar. Res. 48, 591 – 639.
Fay, P. (Ed.), 1983. The Blue – Greens. The Institute of
Biology’s Studies in Biology, London, p. 88.
Franks, P.J.S., 1997. Models of harmful algal blooms. Limnol. Oceanogr. 42, 1273 – 1282.
Fuhrman, J, 1992. Bacterioplankton roles in cycling of organic matter: the microbial food web. In: Falkowski,
P.G., Woodhead, A.D. (Eds.), Primary Productivity and
Biogeochemical Cycles in the Sea. Plenum Press, New
York, pp. 361 – 383.
Fuhrman, J.A., Horrigan, S.G., Capone, D.G., 1988. The
use of 13 N as a tracer for bacterial and algal uptake of
ammonium from seawater. Mar. Ecol. Prog. Ser. 45, 271.
Geider, R.J., 1992. Respiration: taxation without representation. In: Falkowski, P.G., Woodhead, A.D. (Eds.), Primary Productivity and Biogeochemical Cycles in the Sea.
Plenum Press, New York, pp. 333 – 360.
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
Gleitz, M., Grossmann, S., Scharek, R., Smetacek, V., 1996.
Ecology of diatom and bacterial assemblages in water
associated with melting summer sea ice in the Weddell Sea,
Antarctica. Antarctic Sci. 8, 135–146.
Goldman, J.C., Glibert, P.M., 1982. Comparitive rapid ammonium uptake by four species of marine phytoplankton.
Limnol. Oceanogr. 27, 814–827.
Gude, H., 1989. The role of grazing on bacteria in phytoplankton succession. In: Sommer, U. (Ed.), Plankton Ecology. Springer – Verlag, Berlin, pp. 337–364.
Hansen, B., Bjornsen, P.K., Hansen, P.J., 1994. The size ratio
between planktonic predators and their prey. Limnol.
Oceanogr. 39, 395 – 403.
Hessen, D.O., Bjerkeng, B., 1997. A model approach to planktonic stoichiometry and consumer-resource stability.
Freshwater Biol. 38, 447–471.
Horne, A.J., Goldman, C.R., 1994. Limnology. McGraw-Hill,
New York, p. 576.
Jahnke, R.A., Craven, D.B., 1995. Quantifying the role of
heterotrophic bacteria in the carbon cycle: a need for
respiration rate measurements. Limnol. Oceanogr. 40,
436 – 441.
Kishi, M., Ikeda, S., 1986. Population dynamics of ‘red-tide’
organisms in eutrophicated coastal waters — numerical
experiment of phytoplankton bloom in the east Seto Inland
Sea, Japan. Ecol. Model. 31, 145–174.
Lee, S., Fuhrman, J.A., 1987. Relationships between biovolume and biomass of naturally derived marine bacterioplankton. Appl. Environ. Microbiol. 53, 1298.
Legovic, T., Cruzado, A., 1997. A model of phytoplankton
growth on multiple nutrients based on Michaelis–Menton – Monod uptake, Droop’s growth and Liebig’s law.
Ecol. Model. 99, 19 –31.
Levasseur, M.E., Therriault, J.C., 1987. Phytoplankton
biomass and nutrient dynamics in a tidally induced upwelling: the role of NO3:SiO4 ratio. Mar. Ecol. Prog. Ser.
39, 87 – 97.
Lurling, M., Donk, E., 1997. Life history consequences for
Daphnia pulex feeding on nutrient-limited phytoplankton.
Freshwater Biol. 38, 693–709.
McManus, G.B., Fuhrman, J.A., 1988. Clearance of bacteria
sized particles by natural populations of nanoplankton in
the Chesapeake Bay outflow plume. Mar. Ecol. Prog. Ser.
42, 199 – 206.
Monod, J., 1950. La technique de la culture continue: theorie
et applications. Ann. Inst. Pasteur Lille 79, 390–410.
Montealegre, R.J., Verreth, J., Steenbergen, K., Moed, J.,
Machiels, M., 1995. A dynamic simulation model for the
blooming of Oscillatoria agardhii in a monomictic lake.
Ecol. Model. 78, 17 –24.
Nielsen, S.N., 1994. Modelling structural dynamical changes
in a Danish shallow lake. Ecol. Model. 73, 13–30.
Norberg, J., DeAngelis, D., 1997. Temperature effects on
stocks and stability of a phytoplankton–zooplankton
model and the dependence on light and nutrients. Ecol.
Model. 95, 75 – 86.
273
Odum, W.E., Odum, E.P., Odum, H.T., 1995. Nature’s pulsing
paradigm. Estuaries 18, 547 – 555.
Parsons, T.R., Maita, Y., Lalli, C.M., 1984. A Manual of
Chemical and Biological Methods for Seawater Analysis.
Pergamon Press, New York, pp. 101 – 112.
Platt, T., 1986. Primary production of the ocean water column
as a function of surface light intensity: algorithim for remote
sensing. Deep Sea Res. 33: 149 – 163.
Prins, T.C., Escaravage, V., Smaal, A.C., Peeters, J.C.H., 1995.
Nutrient cycling and phytoplankton dynamics in relation to
mussel grazing in a mesocosm experiment. Ophelia 41,
289 – 315.
Prins, T.C., Small, A.C., Dame, R.F., 1998. A review of the
feedbacks between bivalve grazing and ecosystem processes.
Aquat. Ecol. 31, 349 – 359.
Redfield, A.C., Ketchum, B.H., Richards, F.A., 1963. The
influence of organisms on the composition of sea water. In:
Hill, N.M. (Ed.), The Sea. Interscience Publishers, Wiley,
New York, p. 2.
Riegman, R., Mur, L.R., 1984. Regulation of phosphate uptake
kinetics in Oscillatoria agardhii. Arch. Microbiol. 139, 28 –
32.
Riley, G.A., 1946. Factors controlling phytoplankton populations on Georges Bank. J. Mar. Res. 6, 54 – 73.
Riley, G.A., Stommel, H., Bumpus, D.F., 1949. Quantitative
ecology of the plankton of the western North Atlantic. Bull.
Bingham Oceanogr. 12, 1 – 169.
Roelke, D.L., 1997. Managing phytoplankton community composition: can we do it? Department of Oceanography, Texas
A&M University, 298 p.
Roelke, D.L., Cifuentes, L.A., Eldridge, P.M., 1997. Nutrient
and phytoplankton dynamics in a sewage impacted gulf
coast estuary: a field test of the PEG-model and Equilibrium
Resource Competition theory. Estuaries 20, 725 – 742.
Roelke, D.L. and Y. Buyukates, 1999. Synchronization of
Bottom – Up and Top – Down Controls, and ‘Prey-Quality’
Thresholds: a Modeling Study with Management Implications. Young Scientists Conference on Marine Ecosystems
Perspectives, Gilleleje, Denmark, 20 – 24 November.
Roelke, D.L., Eldridge, P.M., Cifuentes, L.A., 1999. A model
of phytoplankton competition for limiting and non-limiting
nutrients: implications for management of dynamic environments. Estuaries 22, 92 – 104.
Savage, A., Knott, B., 1998. Artemia parthenogenetica in Lake
Hayward, Western Australia. I. Interrupted recruitment into
adult stages in response to seasonal limnology. Int. J. Salt
Lake Res. 7, 1 – 12.
Sciandra, A., 1991. Coupling and uncoupling between nitrate
uptake and growth rate in Prorocentrum minimum
(Dinophyceae) under different frequencies of pulsed nitrate
supply. Mar. Ecol. Prog. Ser. 72, 261 – 269.
Shilo, M., 1971. Biological agents which cause lysis of blue –
green algae. Mitteilungen der internationale Vereinigung fur
theoetische und angewandte. Limnology 19, 206 – 213.
Simek, K., Bobkova, J., Macek, M., Nedoma, J., Psenner, R.,
1995. Ciliate grazing on picoplankton in a eutrophic reservoir during the summer phytoplankton maximum: a study
at the species and community level. Limnol. Oceanogr. 40,
1077 – 1090.
274
D.L. Roelke / Ecological Modelling 134 (2000) 245–274
Smayda, T.J., 1978. From phytoplankters to biomass. In:
Sournia, A. (Ed.), Phytoplankton Manual. United Nations
Educational, Scientific and Cultural Organization, Paris, pp.
273 – 279.
Somlyody, L., Koncsos, L., 1991. Influence of sediment resuspension on the light conditions and algal growth in Lake
Balaton. Ecol. Model. 57, 173–192.
Sommer, U. (Ed.), 1989a. Plankton Ecology, Springer–Verlag,
Berling, 364 p.
Sommer, U., 1989b. The role of competition for
resources in phytoplankton succession. In: Sommer, U.
(Ed.), Plankton Ecology. Springer–Verlag, Berling, pp.
57– 106.
Sommer, U., 1992. Phosphorus-limited Daphnia: interspecific
facilitation instead of competition. Limnol. Oceanogr. 37,
966 – 973.
Sommer, U., Gliwicz, Z.M., Lampert, W., Duncan, A., 1986.
The PEG-model of seasonal succession of plankton events
in fresh waters. Arch. Hydrobiol. 106, 436–440.
Sterner, R.W., 1989. The role of grazers in phytoplankton
succession. In: Sommer, U. (Ed.), Plankton Ecology.
Springer – Verlag, Berlin, pp. 107–170.
Sterner, R.W., Hessen, D.O., 1994. Algal nutrient limitation and
the nutrition of aquatic herbivores. Annu. Rev. Ecol. Syst.
25, 1 – 29.
Sterner, R.W., Hagemeier, D.D., Smith, W.L., Smith, R.F.,
1993. Phytoplankton nutrient limitation and food quality for
Daphnia. Limnol. Oceanogr. 38, 871 – 875.
Suttle, C.A., Fuhrman, J.A., Capone, D.G., 1990. Rapid
ammonium cycling and concentration-dependent partitioning of ammonium and phosphate: implications for carbon
transfer in planktonic communities. Limnol. Oceanogr. 35,
424 – 433.
The MathWorks, I., 1997. Matlab 5.0 for Macintosh, 24 Prime
Park Way, Natick, MA 01760-1500.
Tilman, D., 1977. Resource competition between planktonic
algae: an experimental and theoretical approach. Ecology
58, 338 – 348.
Tomas, C.R. (Ed.), 1996. Identifying Marine Diatoms and
Dinoflagellates. Academic Press, New York, p. 598.
Truscott, J.E., 1995. Environmental forcing of simple plankton
models. J. Plankton Res. 17, 2207 – 2232.
Verity, P.G., 1985. Grazing, respiration, excretion, and growth
rates of tintinnids. Limnol. Oceanogr. 30, 1268 – 1282.
Walsh, J.J., 1983. Death in the sea: enigmatic phytoplankton
losses. Prog. Oceanogr. 12, 1 – 86.
Zevenboom, W., Mur, L.R., 1979. Influence of growth rate on
short term and steady state nitrate uptake by nitrate-limited
Oscillatoria agardhii. FEMS Microbiol. Lett. 6, 209 – 212.
Zonneveld, C., 1996. Modelling the kinetics of non-limiting
nutrients in microalgae. J. Mar. Syst. 9, 121 – 136.
.