Ecological Modelling 125 (2000) 203 – 230
www.elsevier.com/locate/ecolmodel
The impact of mixotrophy on planktonic marine ecosystems
H.L. Stickney a,1, R.R. Hood b,*, D.K. Stoecker b
b
a
Swarthmore College, Swarthmore, PA 19081, USA
Uni6ersity of Maryland, Center for En6ironmental Science, Horn Point Laboratory, Cambridge, MD 21613, USA
Accepted 9 August 1999
Abstract
Mixotrophic protists, which utilize a nutritional strategy that combines phototrophy and phagotrophy, are
commonly found in fresh, estuarine, and oceanic waters at all latitudes. A number of different physiological types of
mixotrophs are possible, including forms which are able to use both phototrophy and phagotrophy equally well,
primarily phototrophic phagocytic ‘algae’, and predominantly heterotrophic photosynthetic ‘protozoa’. Mixotrophs
are expected to have important effects on the trophic dynamics of ecosystems, but the exact nature of these effects
is not known and likely varies with physiological type. In order to study the impact that mixotrophs may have on the
microbial food web, we developed mathematical formulations that simulate each of the three aforementioned
physiological types of mixotrophs. These were introduced into idealized, steady-state open ocean and coastal/estuarine environments. Our results indicate that mixotrophs compete for resources with both phytoplankton and
zooplankton and that their relative abundance is a function of the feeding strategy (physiological type and whether
or not they feed on zooplankton) and the maximum growth and/or grazing rates of the organisms. In our models
coexistence of mixotrophs with phytoplankton and zooplankton generally occurs within reasonable parameter ranges,
which suggests that mixotrophy represents a unique resource niche under summertime, quasi-steady state conditions.
We also find that the introduction of mixotrophs tends to decrease the primary production based on uptake of
nitrogen from the dissolved inorganic nitrogen pool, but that this decrease may be compensated for by mixotrophic
primary production based upon organic nitrogen sources. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Mixotrophy; Phototrophy; Phagotrophy; Ecosystem models; Trophic dynamics; Microbial food web; Abundance;
Production
1. Introduction
* Corresponding author. Tel.: +1-410-228-8200; fax: + 1410-221-8490.
E-mail address: [email protected] (R.R. Hood)
1
Present address: Weslyan University, Middletown, CT
06459, USA.
Planktonic protists have traditionally been explicitly classified as either phototrophic phytoplankton or phagotrophic zooplankton on the
basis of the presence or absence of cellular plastids. While the existence of mixotrophs, organisms
which acquire the energy necessary for growth
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PII: S 0 3 0 4 - 3 8 0 0 ( 9 9 ) 0 0 1 8 1 - 7
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H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
and reproduction through a combination of phototrophy and phagotrophy, has long been recognized, until recently these organisms were
considered relatively insignificant exceptions to
the
phytoplankton/zooplankton
dichotomy
(Jones, 1994). The recognition of the ecological
significance of the microbial loop in trophic dynamics in the mid-eighties and the consequent
increase in microbial plankton research, however,
have led to the realization that mixotrophs are
quite common (Sanders, 1991; Jones, 1994;
Riemann et al., 1995; Stoecker, 1998). Mixotrophy has been observed in a number of planktonic
protists, including phytoflagellates, ciliates, and
sarcodines, and is present in eutrophic,
mesotrophic, and oligotrophic waters ranging
from freshwater ponds to the open ocean
(Sanders, 1991; Riemann et al., 1995; Stoecker,
1998).
The extent to which phototrophy and
phagotrophy are employed varies widely among
mixotrophs (Jones, 1994; Holen and Boraas,
1995). Some are primarily autotrophic while others use heterotrophy to fulfill the majority of their
energy requirements. In a recent review paper,
Stoecker (1998) described three general physiological types of mixotrophs: type I, the ‘ideal
mixotrophs’ which are able to utilize phototrophy
and phagotrophy equally well, type II, the primarily phototrophic phagocytic ‘algae’, and type III,
the predominantly heterotrophic photosynthetic
‘protozoa’.
Theoretically, ideal (type I) mixotrophs can successfully grow via autotrophy, heterotrophy, or
mixotrophy. In these mixotrophs, the rate of photosynthesis should be directly dependent upon the
irradiance and the concentration of dissolved inorganic nutrients and inversely related to food
concentration, while the opposite should be true
of the rate of prey ingestion (Fig. 1a). This type of
mixotrophy appears to be surprisingly rare in
natural ecosystems. One example of an organism
that can grow nearly equally well autotrophically
and heterotrophically is the dinoflagellate Fragilidium subglobosum, but this species does not fit
the formulation of model I. Its maximum rate of
mixotrophic growth is higher than the maximum
rate of autotrophic or heterotrophic growth and
the functional relationships of feeding and photosynthesis to irradiance and prey density are not
linear as depicted in Fig. 1 (Skovgaard, 1996;
Hansen and Nielsen, 1997).
The most common forms of the phagocytic
‘algae’ (type II mixotrophs) have the ability to
obtain the inorganic nutrients (nitrogen, phosphorous, and possibly iron) they require for photosynthesis and growth from their prey. They feed
in response to conditions of limiting dissolved
inorganic nutrients. Thus, when dissolved inorganic nutrients are limiting, the rate of photosynthesis should be directly related to food
concentration and the feeding rate should be directly dependent upon irradiance (Fig. 1b).
Mixotrophs that appear to exhibit this behavior
include the dinoflagellates Prorocentrum minimum
(Stoecker et al., 1997) and Gyrodinium
Galatheanum (Li et al., in press), the chrysophytes
Dinobryon cylindricum (Caron et al., 1993) and
Ochromonas minima (Nygaard and Tobiesen,
1993), and the prymnesiophytes Chrysochromulina
polylepis and C. bre6ifilum (Jones et al., 1993).
The predominant photosynthetic ‘protozoa’
(type III mixotrophs) either harbor algal endosymbionts or retain the chloroplasts of their
prey (kleptoplastidy). These mixotrophs supply
the endosymbionts or chloroplasts with nutrients
obtained from their prey and supplement their
carbon budgets with the resulting photosynthates.
Since the nutrients are derived from organic
sources, the rate of photosynthesis should instead
be determined by the feeding rate, which is directly related to prey concentration (Fig. 1c). The
dinoflagellates Noctiluca scintillans (Sweeney,
1971), Amphidinium poecilochroum (Larsen, 1988),
and Pfiesteria piscidia (Burkholder and Glasgow,
1997; Lewitus et al., 1999) and the ciliates Laboea
strobila, plastidic Strombidium spp. (Jonsson,
1987; Stoecker et al., 1988, 1989; Stoecker and
Michaels, 1991) and Perispira o6um (Johnson et
al., 1995) may fit this mixotrophic profile.
Mixotrophs complicate the flow of energy and
nutrients in food webs by functioning as both
producers and consumers, rendering classical
models of marine ecosystems incomplete. Furthermore, conflicting hypotheses concerning the competitive advantages or disadvantages associated
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
205
Fig. 1. (a) ‘Ideal’(type I) mixotrophs: photosynthetic dependence on the concentration of dissolved inorganic nutrients (DIN) and
the food concentration and the dependence of feeding on the concentration of DIN and irradiance; (b) phagocytic ‘algae’ (type II
mixotrophs): dependence of photosynthesis on food concentration and feeding on irradiance under DIN limiting conditions; and (c)
photosynthetic ‘protozoa’ (type III mixotrophs): dependence of photosynthesis on the concentration of DIN and the food
concentration. Adapted from Stoecker (1998).
206
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
with mixotrophy exist. Bockstahler and Coats
(1993a) have suggested that mixotrophs, being
able to utilize both phototrophy and phagotrophy, may have a competitive advantage over absolute autotrophs and heterotrophs. Conversely,
Raven (1997) suggested that mixotrophs may
have lower maximum growth rates than absolute
autotrophs and heterotrophs as a result of the
costs of maintaining photosynthetic organelles,
enzyme systems for the assimilation of inorganic
nutrients, and feeding apparatus. Based on the
latter, mixotrophs should be able to compete with
strict autotrophs and heterotrophs only when
light, nutrients, and prey are limiting (Raven,
1997). Recent chemostat experiments support this
hypothesis (Rothhaupt, 1996).
Although models have been used to consider
interactions between bacterivorous mixotrophs
and bacteria (Thingstad, 1996) or nanophytoflagellates (Barreta-Bekker et al., 1998), to our knowledge this has not been performed for larger
mixotrophic species which are not bacterivorous
(e.g. dinoflagellates, such as Prorocentrum and
Noctiluca, and ciliates such as Laboea). In our
study we theoretically investigate the impact that
mixotrophs which consume other protists may
have on trophic dynamics and we test the aforementioned conflicting hypotheses. How do
mixotrophs affect the relative abundance of dissolved inorganic nutrients, phytoplankton,
zooplankton, and detritus? What effect do
mixotrophs have on primary production and recycling? Does mixotrophy represent an ecological
niche which enables them to coexist with strict
autotrophs and heterotrophs or do they require
special behavioral or life cycle attributes to compete? In order to address these questions, we
formulated mathematical models that represent
the three previously described physiological types
of mixotrophs, introduced each of them into a
nitrogen, phytoplankton, zooplankton, and detritus (NPZD) ecosystem model, and then studied
the impact on the system under steady state conditions. Our models demonstrate that mixotrophs
can have a significant impact upon biomass, production and recycling in aquatic systems. In addition, our results suggest that mixotrophy does not
necessarily confer a competitive advantage over
strict autotrophs or heterotrophs, but rather it
provides a unique ecological niche which allows
coexistence under steady state conditions.
2. The models
The four ecosystem models used to investigate
the impact of mixotrophy in this study are described below. The first is a four-compartment
NPZD model that simulates the processes of an
ecosystem without mixotrophs, while the others
include a mixotroph compartment formulated to
represent one of three general forms of
mixotrophs described above. The various light
and nutrient conditions under which the models
were run and the determination of the ‘realistic’
parameters for mixotrophs II and III are also
explained.
All models were run on Stella II computer
software (High Performance Systems Inc., version
3.0.5) and copies can be obtained upon request
from the corresponding author (R. Hood).
2.1. Four-compartment model
The autotrophic and heterotrophic processes of
a marine ecosystem lacking mixotrophy were simulated with a four compartment microbial food
web model similar to that described in McCreary
et al. (1996). The model is comprised of four
compartments, namely dissolved inorganic nitrogen (DIN), phytoplankton (P), microzooplankton
(Z), and detritus (D), with the abundance of each
expressed in units of nitrogen concentration (mM
nitrogen) (Fig. 2a). All forms of dissolved inorganic nitrogen in the ecosystem, including nitrate
(NO3), nitrite (NO2), and ammonium (NH+
4 ), are
represented by the DIN compartment. The phytoplankton exhibit a light and concentration dependent absorption of nitrogen and a linear rate of
natural senescence, while the omnivorous
zooplankton consume phytoplankton, detritus,
and other zooplankton indiscriminantly. The detritus compartment receives contributions of particulate material from phytoplankton (senescence)
and zooplankton (egestion/mortality) and is thus
composed of both fecal and non-fecal organic
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
207
direct remineralization of dissolved organic nitrogen released from senescing phytoplankton [(1−
b)senescence, below]. Changes in the nitrogen
accumulating within the four compartments as a
result of these biological processes are modeled as
follows:
dN/dt = (AEpz − GEpz)grazingpz
+ (AEdz − GEdz)grazingdz
+ (AEzz − GEzz)predationz
+ remineralization+ (1− b)senescence
− uptakep
(1)
dP/dt = uptakep − senescence− grazingpz
(2)
dZ/dt = GEpzgrazingpz + GEdzgrazingdz
+ (GEzz − 1)predationz
(3)
dD/dt = (1−AEpz)grazingpz
+ (1− AEzz)predationz + bsenescence
− AEdzgrazingdz − remineralization
(4)
where
uptakep
Fig. 2. Stella diagram schematic of (a) the four compartment
model and (b) a basic mixotroph model. Boxes represent the
total nitrogen contained within the dissolved inorganic nitrogen (DIN), phytoplankton, zooplankton, detritus, or
mixotroph stocks in the ecosystem. The arrows with circles
denote the flows of nitrogen between the various stocks.
(PhotoX= nitrogen is removed from the DIN pool through
photosynthesis by phytoplankton (X= P) or mixotrophs (X=
M); GrazXY= nitrogen is transferred from phytoplankton
(X= P), mixotrophs (X =M), or detritus (X =D) to
zooplankton (Y =Z) or mixotrophs (Y =M) via grazing;
PONx=particulate organic nitrogen passes from phytoplankton (X =P), mixotrophs (X = M), or zooplankton (X= Z) to
the detritus pool as a result of phytoplankton senescence or
egestion of a grazing organism; DONx= dissolved organic
nitrogen passes from phytoplankton (X =P) or mixotrophs
(X = M) to the detritus pool as a result of phytoplankton
senescence or excretion of a grazing organism)
matter. Remineralization of this detritus occurs
linearly. Bacteria are not specifically modeled, but
their effect is incorporated into the system
through the detrital remineralization rate and the
= light- and concentration-dependent uptake
of DIN by phytoplankton
= mmp(1− e − I/Ik)(DIN/(DIN +PKs))P
(5)
grazingpz
= grazing of zooplankton on phytoplankton
= (GmpZc*pzP)/o
*z
(6)
grazingdz = grazing of zooplankton on detritus
= (GmpZc*dzD)/o
*z
(7)
predationz
= predation of zooplankton on other zooplankton
= (Gmp(Z 2)c*zz)/o
*z
(8)
*
oz = *c pzP + *c zzZ+ *c dzD+Zks
(9)
remineralization= detrital remineralization
= eD
(10)
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
208
senescence= senescence of phytoplankton
=sP
(11)
AEiz and GEiz are the assimilation and growth
efficiencies, respectively, of zooplankton on phytoplankton (i=p), zooplankton (i=z), and detritus (i= d). *c iz denotes the zooplankton feeding
preferences (which sum to 1). Values for the constants mmp, Gmp, e, s, PKs, ZKs, AEii, GEii, and *c ii
are based upon published values and are listed in
Table 1.
A fifth compartment was added to the above
model to generate models of marine ecosystems in
which mixotrophy is found (Fig. 2b). In general,
the mixotrophs exhibit a light and concentration
dependent absorption of nitrogen similar to that
of the phytoplankton, consume phytoplankton
and other mixotrophs, serve as an additional food
source for the microzooplankton, and contribute
particulate matter to the detritus compartment
through egestion and mortality. The exact construct of the mixotroph compartment, however,
varies with the mixotroph type.
2.2. Mixotroph I
Mixotroph I (the ideal mixotroph) is formulated to obtain its maximum growth rate by a
Table 1
Parameter descriptions, symbols, values, and units for the four ecosystem models
Description
Symbol
Value
Units
Detritus remineralization rate
Growth efficiency for Z on P
Growth efficiency for Z on M
Growth efficiency for Z on Z
Growth efficiency for Z on D
Growth efficiency for M on P
Growth efficiency for M on M
Growth efficiency for M on Z
Assimilation efficiency for Z on P
Assimilation efficiency for Z on M
Assimilation efficiency for Z on Z
Assimilation efficiency for Z on D
Assimilation efficiency for M on P
Assimilation efficiency for M on M
Assimilation efficiency for M on Z
Partitioning of P senescence
Maximum phytoplankton growth rate
Light saturation parameter
Saturation constant for DIN uptake
Phytoplankton senescence rate
Zooplankton maximum grazing rate
Saturation constant for zooplankton grazing
Zooplankton preference for P
Zooplankton preference for M
Zooplankton preference for Z
Zooplankton preference for D
Mixotroph preference for P
Mixotroph preference for M
Mixotroph preference for Z
E
GEpz
GEmz
GEpz
GEdz
GEpm
GEmm
GEzm
AEpz
AEmz
AEzz
AEdz
AEpm
AEmm
AEzm
b
mmp
Ik
PKs
S
Gmz
ZKs
*c pz
*c mz
*c zz
*c dz
*c pm
*c mm
*c zm
0.05
0.30
0.30
0.30
0.15
0.30
0.30
0.30
0.75
0.75
0.75
0.375
0.75
0.75
0.75
0.50
2.00
75.0
0.086
0.05
3.20
0.80
1/3 (1/4)a
1/3 (1/4)a
1/3 (1/4)a
1/3 (1/4)a
1/2 (0.42)b
1/2 (0.42)b
– (0.16)b
Day−1
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Day−1
W/m2
mmol/kg-sw
Day−1
Day−1
mmol/kg-sw
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
a
Figures in parentheses refer to constants in the mixotroph models; those outside the parentheses denote constants used in the
four-compartment model.
b
Figures in parentheses refer to constants in the mixotroph models that include mixotrophic grazing on zooplankton; those
outside the parentheses denote constants used in the mixotroph models in which the mixotrophs do not graze on zooplankton.
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
combination of phototrophy and phagotrophy. It
utilizes the nutritional strategy (photo- or
phagotrophy) giving it a higher growth rate (m
or Gh, respectively) and then attempts to reach
its maximum growth rate through supplementation with the other. The time-dependent nitrogen content of the mixotroph compartment is
thus the sum of the nitrogen taken up and utilized
in photosynthesis and that obtained by the
ingestion of phytoplankton and other mixotrophs, minus the nitrogen contained in mixotrophs eliminated through self-predation or consumed by zooplankton. It is determined as
follows:
209
dD/dt =(1−AEpz)grazingpz
+ (1− AEzz)predationz
+ (1− AEpm)grazingpm
+ (1− AEmz)grazingmz
+ (1− AEmm)predationm
+ bsenescence− AEdzgrazingdz
− remineralization
(16)
The three new functions appearing in the above
definition of the mixotroph I model are defined
below.
uptakem = uptake of DIN by mixotroph
dM/dt = uptakem +GEpmgrazingpm
= If m \Gh
+ (GEmm − 1)predationm −grazingmz
(12)
The nitrogen contents of the other compartments
are calculated with equations similar to the corresponding equations in the four compartment
model, but include terms reflecting the uptake and
grazing by and/or the consumption of
mixotrophs. The additional terms are modeled
after those used for similar phytoplankton or
zooplankton activities:
dN/dt =(AEpz − GEpz)grazingpz
Then mM
Else [If m\max(mmm, GEpmGmmI)− Gh
[GEpm = GEmm]
Then (max(mmm, GEpmGmmI)− Gh)M
Else mM]
(17)
where
+(AEdz −GEdz)grazingdz
m
+(AEzz − GEzz)predationz
+(AEpm − GEpm)grazingpm
= rate of light- and concentration-dependent DIN uptake by mixotroph I
+(AEmz −GEmz)grazingmz
= mmmI(1− e − I/Ik)(DIN/(DIN +PKs))
+(AEmm − GEmm)predationm
Gh = total heterotrophic growth rate
+remineralization +(1 −b)senescence
−uptakep − uptakem
(13)
dP/dt = uptakep − senescence −grazingpz
−grazingpm
(14)
dZ/dt = GEpzgrazingpz +GEmzgrazingmz
Ghp = heterotrophic growth rate from
plankton grazing
= (GEpmGmmIc*pmP)/o
*m
(15)
(19)
phyto(20)
Ghm = heterotrophic growth rate from
mixotroph grazing
= (GEmmGmmIc*mmM)/o
*m
+ GEdzgrazingdz
+ (GEzz −1)predationz
= Ghp + Ghm
(18)
*
om = *c mmP + *c mmM+ZKs
(21)
(22)
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
210
concentration. Mathematically, the mixotroph
growth rate determined by irradiance is
grazingpm
=grazing of mixotrophs on phytoplankton
mI = mmmII(1− e − I/Ik)
=If Gh \ m
(25)
and that attained through phototrophy is
Then GhpM/GEpm
mA = mmmII(1− e − I/Ik)(DIN/(DIN +PKs))
(26)
Else [If Gh\max(mmmI, GEpmGmmI)−m
Else [If Gh \ max(mmmI, GEmmGmmI) −m
The rate of nitrogen input to the mixotroph via
prey ingestion must then equal the difference between the above two growth rates. The assimilation efficiency is used in place of the growth
efficiency under the assumption that the
mixotroph would be able to utilize all of the
assimilated nitrogen with the photosynthetic apparatus. Since the assimilation efficiency of
mixotrophs for other mixotrophs and for phytoplankton are equal, it was not necessary to differentiate between the realized grazing rates on the
two (AEpm was arbitrarily used in the generalized
grazing rate):
Then ((max(mmmI, GEmmGmmI) −m)/Gh)
AEpmGrmII = mmmII(1− e − I/Ik)
Then ((max(mmmI, GEpmGmmI) − m)/Gh)
(Ghp/GEpm)M
Else GhpM/GEpm]
(23)
predationm
=predation of mixotrophs on other
mixotrophs
=If Gh \m
Then GhmM/GEmm
(Ghm/GEpm)M
Else GhmM/GEmm]
− mmmII(1− e − I/Ik)
(24)
These functions specify that the principal source
of nitrogen for this mixotroph may be either
uptake from the DIN pool or prey ingestion,
depending upon which feeding strategy enables it
to obtain the higher potential growth rate under
the prevailing conditions. If that strategy alone
can not sustain the mixotroph’s maximum total
potential growth rate, the other nutritional mode
is utilized as a supplementary source of nitrogen.
Constants are defined in Table 1.
2.3. Mixotroph II
The primarily phototrophic mixotroph II was
designed such that when low nitrogen levels prevent the mixotroph from attaining the maximum
phototrophic growth rate allowed by the ambient
light level, the mixotroph ingests prey in order to
provide the photosynthetic apparatus with the
nitrogen required to support the light-determined
photosynthetic rate. The rate of prey ingestion by
the mixotroph is, of course, dependent upon prey
(DIN/(DIN +PKs))
AEpmGrmII = mmmII(1− e
− I/Ik
(27)
)
(1− (DIN/(DIN + PKs)))
(28)
The realized grazing rate of mixotroph II, which
replaces GmmII in previously defined terms, is then
GrmII = (mmmII/AEpm)(1 − e − I/Ik)
(1−DIN/(DIN +PKs))
(29)
However, the realized grazing rate of
mixotroph II must not exceed the maximum grazing rate of the mixotroph. Thus,
GrmII = If ((mmmII/AEpm)(1 − e − I/Ik)
(1−DIN/(DIN + PKs)))\ GmmII
Then GmmII
Else (mmmII/AEpm)(1 − e − I/Ik)
(1− DIN/(DIN + PKs))
(30)
The mathematical formulation for the nitrogen
content of the mixotroph II compartment is then
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
dM/dt = uptakem +AEpmgrazingpm
211
dD/dt =(1−AEpz)grazingpz
+ (AEmm − 1)predationm −grazingmz
(31)
where uptakem, grazingpm, and predationm are
saturation functions modeled after similar terms
found in the four-compartment model.
+ (1− AEzz)predationz
+ (1− AEpm)grazingpm
+ (1− AEmz)grazingmz
+ (1− AEmm)predationm
uptakem
+ bsenescence− AEdzgrazingdz
= light- and concentration-dependent uptake of DIN by phytoplankton
− remineralization
= mmmII(1− e − I/Ik)(DIN/(DIN +PKs))M
(38)
2.4. Mixotroph III
(32)
grazingpm
= grazing of mixotrophs on phytoplankton
= (GrmIIMc*pmP)/o
*m
(33)
predationm
= predation of mixotrophs on other mixotrophs
= (GrmII(M 2)c*pm)/o
*m
(34)
The remainder of the ecosystem model is similar to that for mixotroph I, although the
mixotroph has no excretion term (AE − GE) because the assimilation efficiency was used instead
of the growth efficiency in determining the
amount of nitrogen obtained by the mixotroph
via its prey:
dN/dt = (AEpz − GEpz)grazingpz
=[GEmm + [(AEmm − GEmm)(1 − e − I/Ik)]]
+(AEmz −GEmz)grazingmz
+remineralization +(1 −b)senescence
(35)
dP/dt = uptakep −senescence −grazingpz
(36)
dZ/dt = GEpzgrazingpz +GEmzgrazingmz
(40)
The formulation of the ecosystem is similar to
those described above, with the uptake, predation,
and grazing terms taken from mixotroph II and
gross growth efficiencies replacing the growth efficiencies found in the mixotroph I ecosystem.
dM/dt = GGEpmgrazingpm
+ GEdzgrazingdz
+ (GEzz −1)predationz
(39)
GGEmm = gross growth efficiency of mixotrophs
consuming other mixotrophs
+(AEzz − GEzz)predationz
− grazingpm
GGEpm = gross growth efficiency of
mixotrophs consuming phytoplankton
= [GEpm + [(AEpm − GEpm)(1 − e − I/Ik)]]
+(AEdz −GEdz)grazingdz
−uptakep − uptakem
Mixotroph III, the primarily heterotrophic
mixotroph, was constructed such that it consumes
phytoplankton and mixotrophs as zooplankton
do, and uses photosynthesis to convert the nitrogen that would normally be excreted (AExm −
GExm) to necessary nitrogen compounds when
light conditions permit photosynthesis to occur.
In order to create the mixotroph III ecosystem,
gross growth efficiencies (GGExm), which incorporate the nitrogen of the prey that was converted
into photosynthates ((AExm − GExm)(1 − e − I/Ik))
as well as that utilized directly (GExm), replaced
the growth efficiencies used for the mixotrophs in
the previous models (GExm). These gross growth
efficiencies are:
+ (GGEmm − 1)predationm − grazingmz
(37)
(41)
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
212
dN/dt =(AEpz − GEpz)grazingpz
Mixotroph Iz
dM/dt =uptakem + GEpmgrazingpm
+(AEdz −GEdz)grazingdz
+(AEzz − GEzz)predationz
+ (GEmm − 1)predationm
+(AEpm − GGEpm)grazingpm
+ GEzmgrazingzm − grazingmz
+(AEmm − GGEmm)predationm
dN/dt = (AEpz − GEpz)grazingpz
+(AEmz −GEmz)grazingmz
+ (AEdz − GEdz)grazingdz
+remineralization +(1 −b)senescence
+ (AEzz − GEzz)predationz
−uptakep
(42)
+ (AEpm − GEpm)grazingpm
+ (AEmz − GEmz)grazingmz
dP/dt = uptakep −senescence −grazingpz
− grazingpm
+ (AEmm − GEmm)predationm
(43)
+ (AEzm − GEzm)grazingzm
dZ/dt = GEpzgrazingpz +GEmzgrazingmz
+ remineralization
+ GEdzgrazingdz
+ (GEzz −1)predationz
(44)
+ (1−b)senescence − uptakep − uptakem
(47)
dP/dt = uptakep − senescence− grazingpz
dD/dt = (1 −AEpz)grazingpz
− grazingpm
+(1−AEzz)predationz
(48)
dZ/dt = GEpzgrazingpz + GEmzgrazingmz
+(1−AEpm)grazingpm
+ GEdzgrazingdz
+(1−AEmz)grazingmz
+ (GEzz − 1)predationz − grazingzm
+(1−AEmm)predationm
(49)
+bsenescence −AEdzgrazingdz
−remineralization
(46)
dD/dt = (1− AEpz)grazingpz
(45)
+ (1− AEzz)predationz
+ (1− AEpm)grazingpm
2.5. Mixotrophic grazing on zooplankton
+ (1− AEmz)grazingmz
Since several mixotrophs are known to graze on
zooplankton (Caron and Swanberg, 1990; Anderson, 1993; Bockstahler and Coats, 1993a,b; Jacobsen and Anderson, 1996; Jeong et al., 1997;
Uchida et al., 1997), each of the above physiological types of mixotrophs was also formulated with
a zooplankton grazing term similar to its self-predation and phytoplankton grazing terms, although the mixotrophs have a lower preference
for the zooplankton (0.16) than for either phytoplankton (0.42) or other mixotrophs (0.42). These
mixotroph models will henceforth be designated
as Iz, IIz, and IIIz. The other ecosystem equations
were changed accordingly. The modified ecosystem formulations are as follows:
+ (1− AEzm)grazingzm
+ (1− AEmm)predationm
+ bsenescence− AEdzgrazingdz
− reminearlization
(50)
where
grazingzm
= grazing of mixotrophs on zooplankton
= If Gh \ m
Then GhzM/GEzm
Else [If Gh \ max(mmmI, GEzmGmmI)− m
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
Then ((max(mmmI, GEzmGmmI) − m)/Gh)
+ (GGEmm − 1)predationm − grazingmz
(58)
(Ghz/GEzm)M
Else GhzM/GEzm]
213
(51)
dN/dt = (AEpz − GEpz)grazingpz
Mixotroph IIz
+ (AEdz − GEdz)grazingdz
dM/dt = uptakem +AEpmgrazingpm
+ (AEzz − GEzz)predationz
+ (AEpz − GEpm)grazingpm
+ (AEmm − 1)predationm
+ AEzmgrazingzm −grazingmz
(52)
+ (AEzm − GGEzm)grazingzm
+ (AEmm − GGEmm)predationm
dN/dt = (AEpz − GEpz)grazingpz
+(AEdz −GEdz)grazingdz
+ (AEmz − GEmz)grazingmz
+(AEzz − GEzz)predationz
+ remineralization
+(AEmz −GEmz)grazingmz
+ (1− b)senescence − uptakep
+remineralization +(1 −b)senescence
−uptakep − uptakem
(53)
dP/dt = uptakep −senescence −grazingpz
− grazingpm
dZ/dt = GEpzgrazingpz +GEmzgrazingmz
(54)
dP/dt = uptakep − senescence− grazingpz
− grazingpm
(60)
dZ/dt = GEpzgrazingpz + GEmzgrazingmz
+ GEdzgrazingdz
+ GEdzgrazingdz
+ (GEzz − 1)predationz − grazingzm
(61)
+ (GEzz −1)predationz −grazingzm
(55)
dD/dt = (1 −AEpz)grazingpz
dP/dt = (1− AEpz)grazingpz
+ (1− AEzz)predationz
+(1−AEzz)predationz
+ (1− AEpm)grazingpm
+(1−AEpm)grazingpm
+ (1+ AEmz)grazingmz
+(1−AEmz)grazingmz
+ (1− AEzm)grazingzm
+(1−AEzm)grazingzm
+ (1− AEmm)predationm
+(1−AEmm)predationm
+ bsenescence− AEdzgrazingdz
+bsenescence −AEdzgrazingdz
−remineralization
(59)
− remineralization
(56)
where
Table 2
Light and nutrient conditions for the ‘open ocean’ and
‘coastal/estuarine’ environments
grazingzm
= grazing of mixotrophs on zooplankton
= (GrmIIMc*zmZ)/o
*m
(57)
Mixotroph IIIz
dM/dt = GGEpmgrazingpm +GGEzmgrazingzm
Environment
Light conditions
Nutrient conditions
Open ocean
Coastal/estuarine
98 W/m2
90 W/m2
5 mM nitrogen
35 mM nitrogen
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
214
where
= (124.7/1)( − 1/0.7)(e − 0.71 − 1)
GGEzm =gross growth efficiency of mixotrophs consuming zooplankton
=89.68 W/m2
= [GEzm +[(AEzm −GEzm)(1 −e − I/Ik)]]
(63)
grazingzm
= grazing of mixotrophs on zooplankton
*m
= (GmmIIIMc*zmZ)/o
(64)
2.6. Light and total nitrogen conditions
I0 = 290 W/m 0.43=124.7 W/m
2
(65)
The midsummer average irradiances were calculated by integrating the exponential decay of light
over the mixed layer depth and dividing by that
depth:
&
Open ocean
Iave =
I0e − kz dz
,
z
=(I0/z)( − 1/k)(e − kz −1)
=(124.7/5)( −1/0.1)(e − 0.15 −1)
=98.13 W/m2
Coastal/estuarine
Iave =
&
I0e − kz dz
(66)
,
z
Total nitrogen levels (5 mM N in the open
ocean case and 35 mM N in the coastal/estuarine
case) were chosen such that the biomasses of
phytoplankton and DIN found at equilibrium in
the four compartment model generally reflect
biomasses observed in the corresponding natural
environment during summer.
2.7. Realistic parameters
The models described above were run under
two different light and nutrient conditions, which
are referred to as the ‘open ocean’ and the
‘coastal/estuarine’ cases (Table 2). Light conditions were determined by calculating the midsummer average irradiance in the mixed layer,
assuming a mixed layer depth of 5 m and an
attenuation coefficient k =0.1 m − 1 in the open
ocean and a mixed layer depth of 1 m and an
attenuation coefficient k =0.7 m − 1 in coastal/estuarine waters. For both cases, the initial irradiance I0 was ascertained assuming a temperate
latitude daily average summer surface irradiance
of 290 W/m2 and a PAR (photosynthetically active radiation) factor of 0.43 at the surface of the
water:
2
(67)
Equilibrium solutions of the type II and III
mixotroph models were found for ‘realistic’
parameters and are described in Section 3.3.
These ‘realistic’ parameters consist of autotrophic
growth rates and heterotrophic grazing rates determined from literature data (Table 3).
A realistic maximum phototrophic growth rate
was determined for mixotroph II from the autotrophic growth rate of 1.13 div d − 1 at 26.5°C,
33 psu, and 475 W/m2 reported by Grzebyk and
Berland (1996) for Prorocentrum minimum. Since,
mI = mmmII(1− e − I/Ik)
[assuming abundant DIN]
(68)
1.13 d − 1 = mmmII(1− e − 475/75)
(69)
mmmII = 1.13 d − 1/(1− e − 475/75)= 1.13 d − 1
(70)
A maximum grazing rate was not calculated for
mixotroph II because changing the maximum
grazing rate had no effect on the equilibrium
solution of the models as long as the grazing rate
exceeded the equilibrium realistic grazing rate of
0.60 d − 1 in the open ocean model and 0.45 d − 1
in the coastal/estuarine case. This is a result of the
fact that the maximum grazing rate appears in the
realized grazing rate equation only as an upper
boundary, not as a factor. GmmII was instead
assumed to equal the zooplankton maximum
grazing rate of 0.60 d − 1.
A maximum phototrophic growth rate was not
determined for mixotroph III as such a growth
rate is not included in the model. The maximum
grazing rate was calculated from the ingestion rate
of 679 pg C cell − 1 h − 1 reported by Stoecker et al.
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
Table 3
‘Realistic’ phototrophic growth rates and heterotrophic grazing rates for mixotrophs II and III
Mixotroph type Maximum phototrophic growth rate
(mmm)
Mixotroph II
Prorocentrum
minimum
1.13 d−1
Mixotroph III
Laboea strobilia –
215
0.60 d−1
solutions of mixotroph models II and III run with
the ‘realistic’ phototrophic growth rate and/or
grazing rate parameters derived from P. minimum
and L. Strobila are also presented (Section 3.3).
Finally, we show how the inclusion of zooplankton as an additional food source for the
mixotrophs (models Iz, IIz, and IIIz) alters these
results (Section 3.4).
2.09 d−1
3.1. Coexistence of mixotrophs, phytoplankton,
and zooplankton
Maximum grazing rate (Gmm)
(1988) for the ciliate Laboea strobila at a prey
concentration of 204 mg C l − 1, and a light intensity of 100 W/m2, similar to the irradiances used
in the models. Using the volume of 78103 mm3
reported for the ciliate at an irradiance of 120
W/m2 and an algal concentration of 140 mg C l − 1
(the conditions closest to those at which the ingestion rate was determined for which a volume was
given) and the conversion 1 mm3 =0.1 pg C employed by Stoecker et al. (1988) [but see also Putt
and Stoecker (1989)].
GmmIII
= (697 pg C cell − 1 h − 1)(1 cell/(78103 mm))
(1 mm/0.1 pg C)(24 h/d) =2.09 d − 1
(71)
3. Results
Phototrophic growth rate and heterotrophic
grazing rate ranges which allow the coexistence of
mixotrophs and phytoplankton in the open ocean
and coastal/estuarine environments are described
for models I, II, and III (without mixotrophic
consumption of zooplankton) in Section 3.1. In
Section 3.2, we report the equilibrium solutions
found for each of the three mixotroph systems in
both environments at three different growth and
grazing parameterizations allowing coexistence
and compare these results with those of the original four compartment model which does not contain a mixotroph component. The equilibrium
The coexistence of mixotrophs, phytoplankton,
and zooplankton depends on how the
mixotrophic grazing and uptake parameters are
defined (Table 4). With a maximum grazing rate
of 3.20 d − 1, coexistence between mixotroph I,
phytoplankton, and zooplankton in an open
ocean and a coastal/estuarine environment occurs
with a mixotrophic maximum phototrophic
growth rate between 0 and 1.4 d − 1. Within these
ranges, the equilibrium biomass of the mixotrophs
generally increases and that of the phytoplankton
decreases as the maximum phototrophic growth
rate increases. Above the maximum phototrophic
growth rate range, the mixotrophs out-compete
the phytoplankton and drive their biomass to
zero.
When the maximum phototrophic growth rate
is arbitrarily set to 0.50 d − 1, coexistence is found
with mixotrophic grazing rates ranging from 1.2
to greater than 10 d − 1 in the open ocean and
from 2.4 to above 10 d − 1 in the coastal/estuarine
environment. Below these ranges, the mixotrophic
biomass falls to zero, while above 10 d − 1, both
the mixotrophs and phytoplankton eventually disappear, presumably as a result of overgrazing on
the part of the mixotrophs. Two different equilibrium ‘states’ exist within these grazing rate
ranges. With a grazing rate at or below 4.2 d − 1 in
the coastal/estuarine environment, the pool of
dissolved inorganic nitrogen is low and the
biomasses of phytoplankton and mixotrophs are
high, while at or above 4.3 d − 1 the opposite
occurs. It appears that with a maximum grazing
rate above 4.3 d − 1 the growth rate resulting from
prey ingestion of the mixotrophs is higher than
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
216
Table 4
Ranges of maximum phototrophic growth rates and maximum grazing rates in which the coexistence of phytoplankton,
zooplankton, and mixotrophs occurs
Ecosystem model
Maximum phototrophic growth rate (mmm) range
Maximum grazing rate (Gmm) range
w/M grazing on Z
Mixotroph I
Open ocean
Coastal/estuarine
0–1.4 d−1
0–1.4 d−1
0–0.5 d−1
0–1.2 d−1
Mixotroph II
Open ocean
Coastal/estuarine
1.0–1.3 d−1
1.1–1.4 d−1
1.0–1.1 d−1
1.1–1.3 d−1
Mixotroph III
Open ocean
Coastal/estuarine
–
–
–
–
their phototrophic growth rate. The mixotrophs
immediately begin ingesting phytoplankton and
other mixotrophs at a rate sufficient to preclude
both blooms, thus leading to a high level of DIN.
High DIN levels then enable the mixotrophs to
utilize photosynthesis to an extent that prevents
their population from decreasing to a size that
allows the phytoplankton population to recover.
In the open ocean environment, no stable equilibrium solution is found when the grazing rate of
the mixotroph falls between 0.9 and 1.1 d − 1. The
system is driven by a predator-prey oscillation
between the mixotrophs and the phytoplankton
— both the phytoplankton and the mixotrophs
bloom initially, but as the DIN decreases the
mixotrophs prey increasingly on the phytoplankton. High mixotroph grazing rates cause the phytoplankton population to crash, leading to
increased self-predation among the mixotrophs.
The consequent mixotroph population crash allows the phytoplankton biomass to rise, which in
turn provides abundant food for the mixotrophs
and allows their population to increase, continuing the cycle. At grazing rates of 1.2 d − 1 and
above, however, stable equilibrium solutions are
found. As the grazing rate of the mixotrophs
increases and the producer biomass decreases
there is a gradual transition to high DIN.
Coexistence between mixotroph II, phytoplankton, and zooplankton occurs when the mixotrophs are parameterized with a maximum pho-
w/M grazing on Z
1.2–10 d−1
2.4–10 d−1
1.2–4.2 d−1
2.4–4.2 d−1
]0.5 d−1
]0.5 d−1
]0.5 d−1
]0.5 d−1
1.4 #3.8 d−1
1.4 #2.3 d−1
1.4 #4.5 d−1
1.3 #2.3 d−1
totrophic growth rate between 1.0 and 1.3 d − 1 in
the open ocean case and 1.1 and 1.4 d − 1 in the
coastal/estuarine system (with a set maximum
grazing rate=3.2 d − 1). Within these ranges, the
biomass of mixotrophs increases and that of the
phytoplankton decreases as the maximum phototrophic growth rate rises. Above these ranges,
the mixotrophs out-compete the phytoplankton
and drive the phytoplankton biomass to zero.
Self-predation and zooplankton grazing drive the
mixotroph population extinct below these ranges.
Coexistence occurs in both environments
whenever the maximum grazing rate is greater
than 0.5 d − 1 (with a set maximum phototrophic
growth rate= 1.1 d − 1). For reasons discussed in
the model section, there was no upper limit on the
grazing rate. However, the mixotrophs disappeared if the maximum mixotrophic grazing rate
fell below 0.5 d − 1.
No phototrophic growth rate range was determined for mixotroph III because a maximum
phototrophic growth rate does not appear in its
formulation. Stable coexistence of phytoplankton,
zooplankton and mixotroph III is found when the
maximum grazing rate is between 1.4 and 3.8
d − 1 in the open ocean and 1.4 and 2.3 d − 1 in
the coastal/estuarine ecosystem. Within these
ranges, the biomass of mixotrophs increases and
that of phytoplankton decreases as the maximum
grazing rate increases. The mixotrophs disappear
as a result of competition from the phytoplankton
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
below these ranges. Above the ranges, the system
is unstable and a predator-prey oscillation, similar
to the one discussed above, appears. However,
damping of the oscillation does occur as the maximum grazing rate rises even higher, leading to
approximately stable equilibriums with extremely
high DIN. The mixotrophs eventually eat both
themselves and the phytoplankton to extinction at
grazing rates far above 10 d − 1.
3.2. Impact of mixotrophy on abundance and
production
The effects the three forms of mixotrophy had
on the open ocean and coastal/estuarine ecosystems were illustrated by running each mixotroph
at three different maximum phototrophic growth
or phagotrophic grazing rates. Figs. 3 and 4
demonstrate that the introduction of mixotrophy
into the open ocean and coastal/estuarine ecosystem models causes changes in the equilibrium
biomasses of the systems which are amplified by
increased mixotrophic biomass. Decreases in phytoplankton biomass are clearly observed upon the
introduction of all three mixotrophs in the open
ocean case (Fig. 3), although the magnitude of the
actual changes in phytoplankton biomass are
somewhat smaller for mixotrophs II and III than
for mixotroph I. Small increases in the detrital
biomass and in DIN and a slight decrease in the
zooplankton biomass also accompany the introduction of mixotrophy. The increase in DIN is
likely a consequence of a decrease in the overall
primary production resulting from the displacement of the phytoplankton producers with
mixotrophs, which both produce and consume.
Phytoplankton displacement by mixotrophs
also accounts, at least in part, for the increase in
detritus. A greater percentage of nitrogen is transferred to the detritus pool than to the DIN pool
through consumption, whereas the amounts of
nitrogen conveyed to the detritus and DIN pools
as a result of senescence are equal. Since the
mixotrophs do not have a senescence term, the
replacement of the phytoplankton with
mixotrophs results in less senescence and more
consumption, causing a larger mass of detritus.
The decrease in zooplankton biomass is proba-
217
bly a result of the change in its food supply. The
decrease in phytoplankton biomass upon the introduction of mixotrophy is not quite matched by
the biomass of the mixotrophs. While the increase
in detritus brings the total biomass of zooplankton prey in the mixotrophic system (phytoplankton, mixotrophs, and detritus) to approximately
the same level as that in the four compartment
model, detritus is a lower quality food for
zooplankton, as the growth efficiency of
zooplankton on detritus is only half that of
zooplankton on phytoplankton or mixotrophs.
The impact the introduction of mixotrophy has
on the coastal/estuarine ecosystem is generally
similar to its impact on the open ocean ecosystem
(Fig. 4), with a few significant exceptions. First,
the DIN dramatically increases when the maximum phototrophic growth rate of mixotroph I
equals 1.40 d − 1, leaving little nitrogen in the
other compartments and disrupting the emerging
trends. Second, the amount of nitrogen in the
DIN compartment tends to drop with the introduction of mixotrophy instead of increase, although the DIN increases as the biomass of the
mixotrophs increases and eventually exceeds the
DIN concentration of the original four compartment model in the cases of mixotroph I and III. It
appears that this irregularity is a result of the
absence of a senescence term. The initial drop in
DIN results from a lower nitrogen flow to the
DIN pool as consumption replaces senescence,
but the increase in detritus eventually compensates for the lower flow as detrital remineralization increases.
These results are rather surprising in the case of
mixotroph III as it resembles zooplankton more
than it does phytoplankton and does not compete
for nutrients with the phytoplankton. One would
expect mixotrophs of type III to impact the population of zooplankton more than that of phytoplankton. However, the phytoplankton and
mixotrophs are food sources of equal quality to
the zooplankton, which consume them without
preference. Zooplankton biomass is not drastically affected because the mixotrophs do not prey
upon zooplankton and the mixotroph biomass
approximately equals the decrease in phytoplankton biomass. The phytoplankton, on the other
218
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
Fig. 3. Effect of mixotrophy on abundance in an open ocean ecosystem. Nitrogen concentrations of the DIN, phytoplankton,
mixotroph, zooplankton, and detritus compartments are shown for the four-compartment NPZD model and each of (a) mixotroph
I (b) mixotroph II and (c) mixotroph III at three different maximum phototrophic growth rates (mmax: a, b) or heterotrophic
grazing rates (Gmax: c). Note the changes in scale between mixotroph models on the graphs displaying the mixotroph and DIN
compartments.
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
Fig. 4. Effect of mixotrophy on abundance in a coastal/estuarine ecosystem; as in Fig. 3 for the open ocean ecosystem.
219
220
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
hand, are consumed by the mixotrophs, resulting
in a lower biomass.
The changes in the phytoplankton and
mixotroph biomasses for the systems containing
mixotroph II tend to complement each other in
absolute numbers and pattern more so than do
the changes accompanying the introduction of the
other two mixotrophs. Additionally, the changes
in the DIN, zooplankton, and detritus are, in
absolute terms, the smallest for that mixotroph
(Figs. 3 and 4). This appears to be a result of the
fact that mixotroph II resembles phytoplankton
more closely than do either mixotroph I or III
and thus the replacement of phytoplankton by
mixotroph II is more complete and has less impact on the system than in the other cases.
Production in the open ocean and coastal/estuarine ecosystems, defined as the amount of nitrogen flowing through each compartment per day, is
also affected by the introduction of mixotrophy
(Figs. 5 and 6). In general, in both ecosystems and
for all mixotroph types the introduction of
mixotrophy causes decreases in DIN, phytoplankton, and zooplankton production and increases in
detrital production. The magnitude of the effect
generally increases with increasing maximum
growth rate (mixotrophs I and II) and grazing
rate (mixotroph III). Deviations from this general
trend, however, are observed for the detrital production of mixotrophs II and III in the open
ocean, for the phytoplankton production of
mixotroph I in the coastal/estuarine environment,
and for the DIN and detrital production of
mixotroph I in both systems.
For the phytoplankton, zooplankton, and detritus, the changes in production effected by the
introduction of mixotrophs reflect the changes
that occur in the nitrogen content of each compartment. DIN production, on the other hand,
generally decreases as DIN concentration increases. This decrease in DIN production reflects
a decrease in primary production (defined here as
the amount of nitrogen taken up by phytoplankton and mixotrophs from the DIN pool) that
occurs as mixotrophs replace the phytoplankton
and as the amount of DIN cycling through the
phytoplankton, zooplankton, and detritus com-
partments decreases. Nevertheless, the total photosynthetic production in the systems containing
mixotrophs II and III does not decrease concurrently with ‘primary production’. A portion of the
nitrogen used in photosynthesis by mixotroph II
and all of that used by mixotroph III is derived
from secondary sources (i.e. prey) and is not
included in ‘primary production’. After accounting for this additional photosynthesis, the changes
in total photosynthetic production (‘primary production’ plus nitrogen obtained from prey) of the
systems containing mixotrophs II and III resemble the pattern observed in DIN production for
mixotroph I, which obtains all of its nitrogen
from the DIN pool. Fig. 7 demonstrates that the
total photosynthetic production of each of the
mixotrophs has a tendency to increase upon the
introduction of mixotrophy, though ‘primary production’ may decrease slightly.
A trend not obvious in Figs. 3–6 is that while
DIN concentration is generally low, DIN production is extremely high and the production of
detritus is much lower than its abundance would
suggest. This is consistent with nitrogen cycling in
a natural ecosystem, where the turnover of dissolved nutrients is rapid and remineralization relatively slow.
3.3. Results of ‘realistic’ parameterizations
When parameter values derived from the literature (Table 3) are used for maximum phototrophic growth rates and/or maximum grazing
rates of mixotrophs II and III, coexistence of
phytoplankton, zooplankton, and mixotrophs is
observed in both environments. The differences in
abundance and production in the two
mixotrophic systems as compared to the four
compartment model are consistent with the general patterns previously discussed (i.e. the principal effect of the introducing mixotrophs is
competition with and displacement of some portion of the phytoplankton population) (Fig. 8).
Fig. 8 also demonstrates that mixotroph II is
significantly more successful in the open ocean
ecosystem than in the coastal/estuarine ecosystem,
while the abundance of mixotroph III is approxi-
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
221
Fig. 5. Effect of mixotrophy on production in an open ocean ecosystem. Production (mM N/day) of DIN, phytoplankton,
mixotrophs, zooplankton, and detritus are shown for the four-compartment NPZD model and each of (a) mixotroph I (b)
mixotroph II and (c) mixotroph III at three different maximum phototrophic growth rates (mmax: a, b) or heterotrophic grazing
rates (Gmax: c). Note the changes in scale between graphs displaying the mixotroph abundance.
222
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
Fig. 6. Effect of mixotrophy on production in a coastal/estuarine ecosystem; as in Fig. 5 for the open ocean ecosystem.
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
mately proportionately equal in the two environments. In nature mixotrophs of physiological type
III, such as L. strobila and other plastidic ciliates,
are common during summer stratification in both
coastal and open ocean waters (Stoecker et al.,
223
1987, 1989, 1994; Putt, 1990; Dolan and Marrase,
1993; Bernard and Rassoulzadegan, 1994), which
is consistent with our model results. Mixotrophs
of type II, including P. minimum, are often common in coastal waters (Bockstahler and Coats,
Fig. 7. Total photosynthetic production of mixotrophs I, II, and III in the (a) open ocean and (b) coastal/estuarine ecosystems and
in the (c) open ocean ecosystem with mixotrophic grazing on zooplankton. Total photosynthetic production is defined as the sum
of all the nitrogen used in photosynthesis per day, including the nitrogen derived from prey as well as that taken up by
phytoplankton and mixotrophs from the DIN pool (‘primary production’).
224
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
Fig. 8. Impact of mixotroph II and III parameterized with realistic maximum phototrophic growth rates (mmax) and/or
heterotrophic grazing rates (Gmax) on the (a) abundances (mM N) and (b) production (mM N/day) of an open ocean and a
coastal/estuarine ecosystems. Mixotroph II: mmax= 1.13 d − 1; mixotroph III: Gmax=2.09 d − 1.
1993a,b; Nygaard and Tobiesen, 1993; Havskum
and Riemann, 1996; Havskum and Hansen, 1997;
Stoecker et al., 1997; Li et al., in press) and are
only sometimes reported from the open ocean,
chiefly under nutrient-limiting conditions (Arenovski et al., 1995), which is the opposite of what
our model suggests.
Additionally, the biomass of phytoplankton exceeds the mixotrophic biomass for both
mixotroph II and III in each environment (Fig. 8).
This predominance of phytoplankton is generally
believed to occur in natural ecosystems, and can
perhaps be attributed to the additional energetic
cost of mixotrophy. This cost is expected to be
highest for type I mixotrophs, which must main-
tain both photo- and phagotrophic appartuses,
intermediate for type II, which may not have to
maintain the phagotrophic apparatus continuously, and lowest for physiological type III, which
borrows the photosynthetic apparatus from its
prey or its endosymbiont although it may have to
provide transport for the inorganic nutrients required for photosynthesis. However, in our
model, type III obtains all its nutrients from its
prey, so transport costs are not applicable here.
3.4. Impact of mixotrophic grazing on zooplankton
The incorporation of terms that reflect
mixotrophic grazing on zooplankton has three
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
major effects. First, the parameter ranges which
allow the stable coexistence of mixotrophs, phytoplankton, and zooplankton contract for
mixotroph Iz and IIz while those for mixotroph
IIIz expand slightly (Table 4). Coexistence of
mixotroph Iz with phytoplankton and zooplankton occurs when the maximum phototrophic
growth rate of the mixotroph is set between 0
and 0.5 d − 1 in the open ocean and 0 and 1.2 d − 1
in the coastal/estuarine case (with a the maximum
grazing rate of 3.2 d − 1) and when the maximum
grazing rate is between 1.2 – 4.2 d − 1 in the open
ocean and 2.4–4.2 d − 1 in the coastal/estuarine
environment (with a maximum phototrophic
growth rate of 0.50 d − 1). Whereas above the
maximum phototrophic growth rate range for
mixotroph I only the phytoplankton disappear,
both the zooplankton and phytoplankton
disappear above the phototrophic growth rate
range for mixotroph Iz. As with mixotroph I, in
the open ocean ecosystem mixotroph model
Iz enters an unstable state slightly below the maximum grazing rate interval (between 0.8 and
1.1 d − 1). However, the high DIN level observed
near the high end of the coexistence intervals
for mixotroph I is not observed with mixotroph
Iz.
For mixotroph IIz the maximum phototrophic
growth rate interval which allows coexistence also
contracts in both the open ocean and coastal/estuarine cases (from between 1.0 and 1.3 d − 1 to
1.0 and 1.1 d − 1, and from between 1.1 and 1.4
d − 1 to 1.1 and 1.3 d − 1, respectively, with a set
maximum grazing rate=3.2 d − 1). Maximum
grazing rate ranges (]0.5 d − 1 for both cases
with a maximum phototrophic growth rate of 1.1
d − 1) remain the same.
In contrast, the maximum grazing rate interval
that allows stable coexistence for mixotroph IIIz
(1.4 and 4.5 d − 1 in the open ocean and 1.3 and
2.3 d − 1 in the coastal/estuarine ecosystem) increases slightly compared to mixotroph III. In
addition, while an interval of unstable coexistence
exists above the grazing rate ranges for
mixotroph III, with the addition of grazing on
zooplankton no such unstable region exists in the
open ocean because the zooplankton disappear
when the maximum grazing rate is above 4.5
225
d − 1. The region of unstable coexistence in the
coastal/estuarine environment is significantly narrower when the mixotrophs consume zooplankton, as the zooplankton disappear when the
maximum grazing rate is above 3.0 d − 1.
The second major result of adding a zooplankton food source is that the previously described
effects on the abundance and production of the
zooplankton and detritus are amplified while the
effects on DIN abundance for mixotrophs Iz and
IIIz are diminished (Fig. 9 for open ocean abundances; trends in oceanic production and in
coastal abundance and production are similar
and thus not shown). However, for mixotroph II
the incorporation of grazing on zooplankton has
little impact, presumably because mixotroph II
depends primarily on phototrophy for its growth.
Finally, the third major effect of incorporating
a zooplankton food source is that it significantly
alters the trends in total photosynthetic production. When mixotrophs I and III consume
zooplankton, the total photosynthetic production
decreases in both the open ocean and coastal/estuarine environments rather than increasing as
was observed when the mixotrophs were modeled
without zooplankton grazing terms. Once again,
the additional grazing terms have little impact on
mixotroph II.
4. Discussion and conclusions
In this paper mathematical formulations have
been presented that describe three basic
mixotrophic feeding strategies. Although the
models are somewhat speculative in detail, the
general strategies we have tried to reproduce for
primarily phototrophic and primarily heterotrophic mixotrophs (types II and III, respectively)
have been observed in a variety of different
planktonic species (see examples cited in the introduction). Our ideal mixotroph I, on the other
hand, does not seem to be well represented in
aquatic ecosystems. Nonetheless, it is interesting
to compare this ideal case with mixotrophs which
are known to exist and speculate as to why it is
not a more prevalent feeding strategy.
226
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
Fig. 9. Effect of mixotrophy on abundance in an open ocean ecosystem. Nitrogen concentrations of the DIN, phytoplankton,
mixotroph, zooplankton, and detritus compartments are shown for the four-compartment NPZD model and each of (a) mixotroph
I (b) mixotroph II and (c) mixotroph III formulated with mixotrophic grazing on zooplankton at three different maximum
phototrophic growth rates (mmax: a, b) or heterotrophic grazing rates (Gmax: c). Note the changes in scale between mixotroph
models on the graphs displaying the mixotroph, DIN, and detritus compartments.
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
In general, the effects of introducing mixotroph
I on the biomass and production of phytoplankton and zooplankton are more pronounced than
the effects of introducing types II and III because
in our model this ideal organism functions equally
well as an autotroph, heterotroph, or some mixture of the two. In addition, Table 4 shows that
our type I mixotroph coexists with strict autotrophs and heterotrophs over a broader range
of phototrophic growth rates than does our type
II mixotroph. Thus, as one might expect, our
ideal mixotroph appears to be a superior competitor with a wider phototrophic niche. However, the
maintenance of both autotrophic and heterotrophic aparatuses may result in a significantly
lower maximum growth rate overall than is calculated by our model (Raven, 1997). These physiological costs may explain why the maximum
phototrophic growth and heterotrophic grazing
rates (0.38 and 1.04 per day, respectively) calculated for Fragilidium subglobosum, which in some
respects fits our type I model, are too low to allow
coexistence in either of our steady state
environments.
The introduction of mixotrophs which consume
only phytoplankton and other mixotrophs into
idealized coastal/estuarine and open ocean systems mainly results in the displacement of a fraction of the phytoplankton. This is the
consequence of a direct competition that exists
between the mixotrophs and the phytoplankton
for nutrient resources and of an additional predation pressure applied on the phytoplankton by the
mixotrophs. There is little effect upon the biomass
of the zooplankton and detritus. However,
mixotrophs which prey on zooplankton as well as
phytoplankton and other mixotrophs have a
greater impact on the ecosystem as a whole. In
addition to a displacement of phtyoplankton
biomass, the introduction of mixotrophs which
also consume zooplankton results in a displacement of a fraction of the zooplankton, and more
pronounced changes (increases) in the amount of
detritus.
For all three physiogical types the magnitude of
the impact of introducing mixotrophy is strongly
dependent upon the growth and grazing characteristics of the mixotrophs. It cannot be concluded
227
that one is intrinsically competitively superior to
the other or that mixotrophs are generally competitively inferior to strict autotrophs or heterotrophs. However, when the mixotrophs which
feed only on phytoplankton and other mixotrophs
are parameterized with maximum phototrophic
growth rates and/or grazing rates of ‘representative’ organisms (Table 3), the biomass of phytoplankton exceeds the biomass of mixotrophs in all
cases (Fig. 8). Thus, under the spatially and temporally uniform conditions of the models,
mixotrophs appear to be competitively inferior.
Of course, if heterogenous environments favor
mixotrophs, as has often been suggested (Bird and
Kalff, 1987; Beaver and Crisman, 1989; Holen
and Boraas, 1995; Stoecker, 1998), our models
will likely underestimate the relative abundance of
mixotrophs. Also, the parameters used in our
models were obtained from organisms we believe
to be representative of each mixotroph type, but
maximum phototrophic growth rates and/or maximum grazing rates vary widely within the groups
and results for any specific mixotroph would vary
as well. In addition, our models do not account
for the effects of attributes such as swimming
behavior. However, the fact that it is not necessary to invoke such mechanisms to explain the
existence and coexistence of mixotrophs is an
important result — our models show that
mixotrophy represents a unique food resource
niche which allows coexistence even in spatially
and temporally uniform environments.
This result is broadly consistent with previous
laboratory and modeling studies. Chemostat experiments with freshwater nanoflagellates have
shown that a mixotrophic bacterivorous nanoflagellate, Ochromonas sp., can coexist with a bacterivorous heterotrophic flagellate when bacteria
and light are supplied simultaneously and with a
photosynthetic flagellate when an inorganic nutrient is limiting and bacteria are present (Rothhaupt, 1996). Thingstad (1996) explored the
coexistence of a bacterivorous mixotrophic flagel
late with an autotrophic flagellate, a heterotrophic
bacterivorous flagellate, and inorganic nutrient
limited bacteria in a chemostat scenario using a
linear analytical model. Although they found no
228
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
equilibrium with all four species simultaneously
present, they suggested that minor modifications,
such as adding saturation kinetics or higher
trophic levels as in our models, could alter the
result. Furthermore, Barreta-Bekker et al. (1998)
addressed the effect of mixotrophy among the
nanophytoflagellates on nutrient and carbon dynamics with a simulation model of the microbial
food web in marine enclosures and concluded that
mixotrophy is an ecological niche in nutrient-depleted environments.
Our model results also suggest that the introduction of mixotrophy leads to decreased primary
production (defined here as the amount of nitrogen taken up by phytoplankton and mixotrophs
from the DIN pool) and recycling (defined as the
amount of nitrogen returning to the DIN pool
from various sources), as evinced by the previously described trend of decreasing DIN production. This indicates that the microbial trophic
system actually becomes less productive as a
whole upon the introduction of any of the three
types of mixotrophy, which runs counter to much
of what has previously been suggested (Sanders,
1991; Barreta-Bekker et al., 1998; Stoecker, 1998).
We define primary production in terms of DIN
uptake because DIN uptake is presumably accompanied by uptake of dissolved inorganic carbon
(DIC) whereas nitrogen obtained from secondary
sources may not be. However, it is important to
emphasize that for mixotrophs which feed only on
phytoplankton and other mixotrophs the total
amount of photosynthesis, which includes photosynthesis that utilizes nitrogen obtained from secondary sources, tends to increase with the
introduction of mixotrophy. Thus, our models
predict that although primary production (as
measured by DIN and DIC uptake) will decrease
upon the introduction of mixotrophy the total
photosynthetic rate can be maintained through
the direct recycling of organic nitrogen that does
not enter the dissolved inorganic pool.
The approach that we have taken, to study the
impact of mixotrophy on an idealized model
ecosystem under steady state conditions, obviously excludes some important biological components of marine ecosystems, such as bacteria.
However, we think it is unlikely that the explicit
inclusion of a bacteria compartment would dramatically alter the main conclusions of our research. Although bacteria are an important food
source for some small mixotrophic species (e.g.
3–5 mm photosynthetic flagellates; Epstein and
Shiaris, 1992; Hall et al., 1993; Havskum and
Riemann, 1996), they are generally not a significant source of nutrients for the larger mixotrophic
species that we focus on in this study (e.g. dinoflagellates such as Prorocentrum and Noctiluca,
and ciliates such as Laboea and other plastidic
oligotrichous ciliates). Thus, our models should
be considered as representative of larger species
which are not bacterivorous. Moreover, our principal interest here is studying how the introduction of mixotrophy affects phytoplankton and
zooplankton biomass and production, and we
have included only those explicit compartments
that we feel are required to do this.
Finally, we emphasize that the basic conclusions from this research are consistent with well
established ecological principles. Our models
show that mixotrophs compete for resources with
both phytoplankton and zooplankton and that
the relative abundance of the mixotrophs is a
function of the feeding strategy (type I, II or III
and whether or not they feed on zooplankton)
and the maximum growth and/or grazing rates of
the organisms. Furthermore, coexistence of
mixotrophs generally occurs within reasonable
parameter ranges; we do not have to invoke unrealistic growth and/or grazing rates or special behavioral attributes for mixotrophs to coexist with
strict autotrophs and heterotrophs. These results,
which are also consistent with laboratory studies,
indicate that mixotrophy provides a unique resource niche which allows coexistence under
steady state summertime conditions in both open
ocean and coastal/estuarine environments.
Acknowledgements
This research was carried out with financial
support from NSF and the Maryland Sea Grant
Research Experiences for Undergraduates program. Additional support was provided by NSF
H.L. Stickney et al. / Ecological Modelling 125 (2000) 203–230
grant OCE 96-28888 to R. Hood and NSF grant
OCE 93-1772 to D.W. Coats and D.K. Stoecker.
We would also like to thank A. Li and A. Skovgaard for helpful discussions on mixotrophy in
dinoflagellates.
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