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Limnol. Oceanogr., 58(1), 2013, 173–184
2013, by the Association for the Sciences of Limnology and Oceanography, Inc.
doi:10.4319/lo.2013.58.1.0173
E
Control of plankton seasonal succession by adaptive grazing
Patrizio Mariani,a,* Ken H. Andersen,a André W. Visser,a Andrew D. Barton,b and Thomas Kiørboe a
a Centre
for Ocean Life, National Institute for Aquatic Resources, Technical University of Denmark, Charlottenlund Castle,
Charlottenlund, Denmark
b Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
Abstract
The ecological succession of phytoplankton communities in temperate seas is characterized by the dominance
of nonmotile diatoms during spring and motile flagellates during summer, a pattern often linked to the seasonal
variation in the physical environment and nutrient availability. We focus on the effects of adaptive zooplankton
grazing behavior on the seasonal succession of temperate plankton communities in an idealized community model
consisting of a zooplankton grazer and two phytoplankton species, one motile and the other nonmotile. The
grazer can switch between ambush feeding on motile cells or feeding-current feeding on nonmotile cells. The
feeding-current behavior imposes an additional mortality risk on the grazer, whereas ambush feeding benefits
from small-scale fluid turbulence. Grazer–phytoplankton feeding interactions are forced by light and turbulence
and the grazer adopts the feeding behavior that optimizes its fitness. The adaptive grazing model predicts essential
features of the seasonal plankton succession reported from temperate seas, including the vertical distribution and
seasonal variation in the relative abundance of motile and nonmotile phytoplankton and the seasonal variation in
grazer abundance. Adaptive grazing behavior, in addition to nutrient and mixing regimes, can promote
characteristic changes in the seasonal structure of phytoplankton community observed in nature.
While these processes certainly affect the growth rates of
phytoplankton and structure the community, grazing-induced
mortality rates also play an important role in shaping the
seasonal succession of phytoplankton communities (Hairston
et al. 1960). Zooplankton grazing is the largest source of
mortality for marine phytoplankton (Calbet and Landry 2004)
and has been shown to affect seasonal dynamics (Lampert
et al. 1986). Moreover, the size structure of phytoplankton
communities is thought to be the consequence of the
interaction between nutrient availability and predator control
(Armstrong 1994). Less is known, however, about how
zooplankton feeding behaviors and phytoplankton community structure are related. In this predator–prey interaction, the
effects go both ways, with grazers shaping the community
structure and phytoplankton community structure eliciting
different feeding strategies in the grazer community. In
particular, grazers are able to adapt their feeding behavior to
the environmental conditions (Kiørboe 2008), with repercussions throughout the plankton ecosystem (Reichwaldt et al.
2004; Kiørboe 2008; Mariani and Visser 2010).
Here, we investigate the two-way interaction between the
motility of the phytoplankton cells and the grazing
behavior of the zooplankton. We do this by developing a
simple model for a temperate plankton community with
one predator, a motile prey, and a nonmotile prey, in which
we analyze the effects of adaptive zooplankton grazing
behavior on the abundance of the two phytoplankton
species. We assume phytoplankton species are identical
except for their motility. They grow in response to seasonal
changes in light and compete for a common carrying
capacity, whereas their losses are determined by zooplankton grazing alone. Zooplankton adopt the feeding strategy
that maximizes its fitness: feeding-current feeding for
nonmotile prey and ambush feeding for motile prey. Each
feeding behavior has quantifiable trade-offs in terms of
The structure of pelagic ecosystems is affected by
physical variability and biological interactions that occur
on multiple temporal and spatial scales (Mann and Lazier
1991). The strength of these interactions is highly variable
and affects the function and dynamics of the food web by
driving the major patterns in species composition, succession, and distribution (Reynolds 1984). Seasonal cycles of
plankton communities are common features of marine
environments. In many temperate regions, a change from
the dominance of diatom species in spring to flagellates and
dinoflagellates during summer has been observed in large
lakes (Reynolds 1984), river estuaries (Turner et al. 1983),
open ocean (Michaels et al. 1994), and coastal marine
systems (D’Alcalà et al. 2004).
Competition for light and nutrients are thought to be
key factors regulating the seasonal succession of phytoplankton (Huisman et al. 1999). Differences in nutrient
affinity and variation in turbulence levels have been used to
explain succession in phytoplankton life forms, as depicted
by Margalef’s mandala (Margalef 1978). Margalef’s paradigm suggests that large, nonmotile cells such as diatoms
benefit from high-nutrient and turbulent conditions;
physical mixing compensates for the sinking loss from the
productive layers and brings nutrients to the surface layer,
allowing for the formation of a spring bloom. In contrast,
motile cells such as flagellates and dinoflagellates benefit
from low-nutrient and stratified conditions in which
turbulence is relatively weak because motility allows
vertical migration and exploitation of nutrients from depth
and light harvesting in the surface. Motility also allows
phytoplankton cells in a relatively quiescent environment
to utilize small-scale patchiness in the distribution of
nutrients (Seymour et al. 2009).
* Corresponding author: [email protected]
173
174
Mariani et al.
predation risk and prey encounter rates. In this model, the
single zooplankton controls the phytoplankton abundance
in a manner consistent with the ‘‘killing the winner’’
hypothesis (Thingstad and Lignell 1997; Thingstad 2000), a
mechanism proposed to have a strong shaping influence on
the structure of aquatic microbial and autotrophic communities (Pernthaler 2005; Winter et al. 2010). The fundamental trade-offs between competition and predator
defense allows for the coexistence of different phytoplankton specialists sharing a common resource. In our model,
‘‘defense specialization’’ assumes a dynamic nature as the
grazer switches feeding mode, preferentially targeting the
specialist that affords it the best advantage in terms of
fitness. We demonstrate that adaptive zooplankton feeding
behavior can lead to a seasonal succession in the
phytoplankton community, from dominance of nonmotile
forms during spring to motile forms during summer, which
resembles the seasonal succession widely observed in
temperate seas.
Model formulation
Zooplankton grazing behavior—We consider a model
system with a zooplankton grazer switching feeding
strategy between ambush and feeding-current modes when
exposed to motile and nonmotile prey, respectively. Such
behavior has been described for copepods (Jonsson and
Tiselius 1990; Kiørboe et al. 1996), and each feeding
behavior has unique costs and benefits. When exposed to
motile prey the grazer adopts a sit-and-wait ambush
strategy where a moving prey is perceived by the
hydromechanical disturbance that it generates (Jonsson
and Tiselius 1990). Alternatively, when nonmotile phytoplankton are available, the grazer generates a feeding
current such that passive prey are transported toward the
grazer (Kiørboe et al. 1996). The feeding current may pull
the grazer through the water at a velocity that approaches
the feeding current speed; hence, there is no clear
distinction between a feeding-current and cruise-feeding
grazer (Kiørboe 2011). Because motile flagellates are often
evasive and may respond to feeding currents by escape
jumps (Jakobsen 2002), they are more likely to be caught
by the ambush feeders. In contrast, nonmotile prey will
rarely encounter an ambush grazer and do not generate a
hydromechanical signal that can be perceived by the grazer.
Thus, the two feeding behaviors are specifically targeting
either motile or nonmotile prey. With regard to its own
mortality risk, active foraging, either by generating a
feeding current or by swimming, generates a strong
hydromechanical signature and increases the predator
encounter speed, thus making an active grazer more
susceptible to predation than an ambush feeding grazer
(Kiørboe 2011). Finally, in the ambush feeding behavior,
the grazer benefits much more from small-scale fluid
turbulence in terms of elevated prey encounter rates than
in the feeding-current behavior (Saiz and Kiørboe 1995;
Kiørboe et al. 1996).
The zooplankton feeding behavior is modeled by a single
trait, t, interpreted as the fraction of time the grazer spends
generating feeding currents. The grazer is constantly
striving to adapt t to maximize its instantaneous fitness
measure. Here, we use the net population growth rate as a
proxy for fitness,
gðtÞ~rðtÞ{dðtÞ
ð1Þ
where r(t) is the reproductive rate and d(t) is the death
rate. An alternative formulation of the fitness measure,
which might appear more realistic at the individual
organism level, is g(t) 5 r(t)/d(t) (Mariani and Visser
2010). However, we show below that using this alternative
formulation of our model yields the same results. Hence,
Eq. 1 is used to simplify the mathematical description of the
fitness gradient.
Population dynamics—We consider a simple and wellstudied two-prey, one-predator system (Vance 1978) in
which a grazer population feeds on two phytoplankton
species, motile and nonmotile. The adaptive grazer (C) can
employ either of two feeding behaviors: feeding-current
feeding on the nonmotile prey (Rn) or an ambush strategy
feeding on moving prey (Rm). The two prey populations
have logistic growth and compete for a common resource
(e.g., nutrients), which is represented by a shared carrying
capacity K,
1 dRm
Rm zRn zC=c
~m 1{
{ba C ð1{tÞ ð2aÞ
Rm dt
K
1 dRn
Rm zRn zC=c
~m 1{
{bc Ct
Rn dt
K
1 dC
~gðtÞ~rðtÞ{dðtÞ
C dt
ð2bÞ
ð2cÞ
~cba Rm ð1{tÞzcbc Rn t{dðtÞ
where m is the growth rate of the two prey species and c is
the growth yield (i.e., number of grazers produced per prey
cell ingested). Motile and nonmotile phytoplankton differ
only in their loss terms (Eqs. 2a,b). The linear relation
between the two feeding strategies accurately describes the
observed behavior of copepods feeding on a mixed diet of
motile and nonmotile prey species (Kiørboe et al. 1996).
We assume a linear functional response with biomass
specific clearance rates ba for the ambush strategy and bc
for the feeding current strategy. These nonsaturating
functional responses are invoked as a simplifying assumption, but we note that this could lead to overestimations of
feeding rates when phytoplankton concentrations are high
(i.e., during bloom). Finally, the mortality rate d of the
grazers is described as a function of the feeding behavior,
dðtÞ~mzpt
ð3Þ
where m is a behavior-independent mortality and pt
represents the additional mortality associated with the
feeding current behavior. For convenience we also include
in here the loss of potential reproductive rate (mathematically the same as a mortality rate) due to the extra
energetic costs of generating a feeding current.
Grazing behavior and plankton community
We note that the assumed form of the logistic term
guarantees mass conservation in the model. Notably, the
limiting factor available for growth is N 5 K 2 Rm 2 Rn 2
C/c; hence, the logistic form in Eqs. (2a,b) is equivalent to
first-order growth kinetics with a growth-based affinity m/K
(Thingstad and Sakshaug 1990). This approximation is
valid in nonsaturating nutrient conditions that likely
prevail in most natural environments, but it could overestimate the uptake rate when nutrient concentrations are
greatest (e.g., in upwelling systems). On the other hand, it
provides a reasonably simple means of including a limiting
resource with minimal model complexity.
To close the system (Eqs. 2, 3), we use a dynamic model
of predator behavior (Abrams and Matsuda 2004; Uchida
et al. 2007) where t changes proportionally to the
individual fitness gradient to maximize fitness,
dt
dg
~k
dt
dt
ð4Þ
where k is a constant determining the speed of behavioral
change and dg/dt is the fitness gradient derived from Eq. 1.
The numerical integration of t in Eq. 4 is obtained by
imposing upper and lower bounds in the interval 0 # t # 1.
A similar approach has been used to analyze evolutionary adaptation (Vincent et al. 1996) and community and
population adaptation (Wirtz and Echkardt 1996; Merico
et al. 2009). In the case of constant prey abundance, solving
Eq. 4 would lead to a single, maximally fit value of t in
which any further change negatively affects the fitness g(t).
However, population dynamics in Eq. 2 alter the values of
Rm and Rn and therefore modify the benefits of a given
predator strategy, subsequently modulating the value of t.
Mechanistic description of the vital rates—The growth
rate m of phytoplankton is assumed to depend on light (I,
mmol m22 s21) and is described by a Monod equation,
m~
aI
1zaI=mMax
ð5Þ
where a is the initial slope of the m2I curve, and mMax is the
maximum growth rate under ideal conditions. Effects of
small-scale fluid turbulence and motility on the growth
rates of phytoplankton are neglected.
When the grazer has an ambush feeding behavior, prey
are perceived by means of hydromechanical sensors, and
the clearance rate is given as
h
i
ð6Þ
ba ~pa21 lðea1 Þ1=3 zu
where a1 is the reaction distance to the prey, u is the velocity
difference between the predator and the swimming prey
(Saiz and Kiørboe 1995), l is a turbulence constant
(Delichatsios and Probstein 1975), and e is the turbulence
dissipation rate. Notably, prey clearance rates for ambush
feeders depend on turbulence, which can vary over many
orders of magnitude in the natural environment, and relative
velocity.
When the grazer is feeding on nonmotile prey (Rn),
passive prey are captured in a capture volume determined
175
by the predator feeding current v and the reaction distance
a2 (Kiørboe 2008). The clearance rate is then (Jonsson and
Tiselius 1990):
bc ~pa22 v
ð7Þ
Turbulent velocities in the pelagic ocean at the scale of
zooplankton are typically much less than feeding current
velocity (Yamazaki et al. 2002). Thus, under typical
conditions, turbulence has little effect on prey encounter
rates for the feeding-current behavior (Kiørboe and Saiz
1995).
Simulation procedure—We link the ecosystem model to
an idealized one-dimensional mixed layer model tuned to
the North Sea (General Ocean Turbulence Model [GOTM];
Burchard et al. 2006). The model has 110 vertical levels, 1 m
spatial resolution, and runs for 1 yr with time step of 1 h
using realistic atmospheric forcings and a k2e turbulence
closure model.
We use the physical model to calculate seasonal
variations in turbulence (e) and light (I) in the upper ocean
layer (Fig. 1) to estimate plankton vital rates, growth (m),
and loss (ba,c), in the integration of Eq. 2. Additionally, we
analyze the plankton vertical transport and the seasonal
cycle, directly coupling the community model to the mixed
layer model to include the effects of vertical transport on
the plankton. We solve the transport and reaction terms
using a split method separating the numerical solution of
the diffusion part and the reaction terms. We also assume
that adaptive behavior has a timescale shorter than the
transport timescale. Additional details on discretization
and numerical integration of the coupled system can be
found in Burchard et al. (2006). From arbitrary low initial
concentrations, the model is integrated forward in time
using physical forcing over a recursive annual cycle until it
reaches a stationary seasonal cycle.
The formulation of the feeding behavior in Eqs. 6 and 7
describes well the experimental results for the copepod
Acartia tonsa, and parameter values for this species are
used (Table 1; Saiz and Kiørboe 1995). From low (e 5
1029 m2 s23) to high (e 5 1025 m2 s23) turbulence
conditions, clearance rates for ambush feeding have values
between ba 5 15 and 105 mL d21, whereas filter feeding
holds steady at bc 5 49 mL d21. These clearance rates
compare well with typical values observed in copepod
communities (Kiørboe 2011). Furthermore, we assume a
constant predator : prey weight ratio of 1000 : 1 (Hansen et
al. 1997) and a growth efficiency of 1 : 3 (Kiørboe et al.
1985), thus equivalent to c 5 3 3 1024. With a grazer body
mass WC 5 8 mg C (a 1 mm copepod; Mauchine 1998), this
implies a phytoplankton cell mass of WR 5 8 ng C and a cell
size of ca. 50 mm diameter (assuming 1027 mg C mm23;
Menden-Deuer and Lessard 2000), typical for large spring
diatoms and later summer dinoflagellates. The typical
winter concentrations of limiting nitrogen nutrients in, for
example, the North Atlantic Ocean, is 10 mmol L21; hence,
the phytoplankton biomass can at most reach 108 cells m23
(at C : N 5 6), which is thus our estimate of the carrying
capacity of the system. To maintain a minimal model, we
176
Mariani et al.
Fig. 1. Time series of (a) light, I, and (b) dissipation rate, e, as derived from the GOTM and
used in the analyses of the dynamics of the population model (thick black lines). I is an interpolating
function of (gray line) daily values of the available short wave radiation averaged over the mixed
layer depth, and e is in the range of (gray line) daily values of dissipation rate averaged over 30 m
depth. The mixed layer depth is calculated using a turbulent kinetic energy threshold of 1025 m2 s22.
As references, monthly averages of (a) short-wave radiation and (b) dissipation rate as derived from
GOTM at 5 m (square), 20 m (dot), and 40 m (triangle) are shown.
choose the cell size to be constant and identical for both
phytoplankton types. Finally, the constant describing
mortality associated with feeding (p) was set to double
the natural mortality rate of the grazer while employing
feeding current behavior (p 5 m). Because this value of p
is not well constrained by empirical evidence, we provide
a sensitivity analysis on this as well as other parameter
choices.
The model calculates abundances of resources (cell m23)
and grazers (individuals m23, henceforth ind. m23), which
are then shown in units of biomass using the conversion
values WR,C.
We assume that zooplankton adapt their feeding behavior
faster than the population dynamics of the plankton
resources. This is controlled by the parameter k, which is a
measure of the ratio between the population dynamics
timescale and the behavioral timescale. In our simulations
we use k 5 10, which leads to a clear separation between the
timescales of population and adaptive dynamics while not
affecting the stability of the dynamic system. All the values
Table 1. Model parameters and sensitivity test expressed as percent variation of the state variables (DC*, DRm , DRn , Dt*) for a 30%
increase in each parameter.
Parameter
Definition and units
Value
DC*
DRm
DRn
Dt*
a
mMax
a1
u
a2
v
c
Initial slope growth curve (d21[mmol m22s21]21)
Maximum growth rate (d21)
Reaction distance to motile prey (cm)
Prey relative velocity (cm s21)
Reaction distance to nonmotile prey (cm)
Feeding current velocity (cm s21)
Conversion efficiency (biomass predators
produced per biomass prey eaten)
Behavior-independent mortality rate (d21)
Predation risk (d21)
Turbulence constant
Carrying capacity (mmol L21)
Adaptive feeding constant
Biomass of individual grazer (mg C)
Biomass of phytoplankton cell (ng C)
1.5 3 1022
1
0.04
0.025
0.015
0.8
3 3 1024
5
6
27
21
23
2
27.5
0
0
243
215
0
0
223
0
0
0
0
241
223
223
0
0
45
12
233
218
0
0.1
0.1
1.37
10
10
8
8
211
23
21
27.5
0
30
0
30
0
211
0
0
0
30
15
15
0
0
0
0
30
0
0
9
0
0
0
0
m
p
l
K
k
WC
WR
Grazing behavior and plankton community
and units of the parameters used in our model simulations
are in Table 1.
Observed data—We compare some of the model
predictions with two independent sets of phytoplankton
observations: a long-term time series near Stonehaven,
Scotland (56u57.89N, 02u06.29W) and Continuous Plankton
Recorder (CPR) data from the North Atlantic.
A detailed reconstruction of the temporal variability of
diatoms and dinoflagellates in a long-term station in the
North Sea near Stonehaven, Scotland, has been presented
in Bresnan et al. (2009). Using monthly abundance data
(cells L21) for diatoms and dinoflagellates in the period
1997–2006, we computed the average seasonal cycle of
abundance over all the years. Accounting for the main
species composition observed in the samples, we then
converted abundance to biomass concentration (mg C m23)
using a constant dinoflagellate and diatom carbon contents
of 0.4 (consistent for Amphidinum sp.) and 0.04 ng C cell21,
respectively (Menden-Deuer and Lessard 2000); the value
for diatoms is consistent with the carbon content per cell of
Thalassiosira and Skeletonema species (Strathmann 1967).
Using constant carbon content excludes effects of changing
species composition over the seasons. Nevertheless, the
approach allows for approximate estimates of the concentrations during bloom and summer conditions for both
diatoms and dinoflagellates.
The CPR has measured the abundances of hundreds of
plankton taxa, including diatoms and dinoflagellates, in the
North Atlantic for more than a half-century (Richardson
et al. 2006). Although CPR data do not include the smallest
cells, such as picoplankton, ecologically and biogeochemically relevant diatom and dinoflagellate taxa are wellsampled by the survey. We consider only those taxa that
were monitored over the entire CPR survey duration and
spatial extent and only dinoflagellate taxa that are known
to be photoautotrophic or mixotrophic, thus excluding
pure heterotrophs. We calculated the mean annual cycle of
CPR abundance for 59 diatoms and 32 dinoflagellates,
averaged over the entire North Atlantic survey area and for
all years within 1958–2006. These abundances are best
considered a semiquantitative measure of phytoplankton
number density at roughly 10 m depth (Richardson et al.
2006).
Results
Fixed point and community structure—The dynamical
system in Eqs. 1–4 has one stable fixed point:
8
m
>
Rm ~
>
>
cba
>
>
>
>
> pzm
>
>
>
< Rn ~ cbc
mðba zbc Þ½Kcba bc {ba p{mðba zbc Þ
>
>
C~
>
>
>
ba bc ½Kcba bc zmðba zbc Þ
>
>
>
>
b
>
a
>
: t ~
ðba zbc Þ
ð10Þ
177
Conditions of light, turbulence, and carrying capacity affect
zooplankton feeding behavior and alter the plankton species
composition at the fixed point. In particular, Rm is a
decreasing function of turbulence through the dependence of
ba on e, whereas Rn is constant under changing light and
turbulence conditions. Hence, the ratio between the equilibrium abundances of motile to nonmotile phytoplankton
(Rm : Rn ) is smaller with greater turbulence, in agreement
with Margalef’s paradigm (Margalef 1978), but for quite
different reasons because we only consider grazing effects in
the model.
Using the parameters in Table 1, we can visualize these
dynamics (Fig. 2). In particular, with increasing turbulence,
Rm declines while Rn remains constant (Fig. 2a). When K ,
Rm + Rn , the concentration of phytoplankton is too low to
support zooplankton. Moreover, zooplankton abundance
(C*) tracks changes in Rm + Rn and it decreases with e and
increases with K (Fig. 2b). On the other hand, the adaptive
trait, t*, tends to increase with e (Fig. 2c). Hence, higher
turbulence favors nonmotile plankton and more feedingcurrent feeding. These relations between turbulence and
plankton community are general and independent of the
particular values of the parameters we use.
It is noteworthy that coexistence among the phytoplankton does not occur in the absence of adaptive grazing
(Vance 1978). The stability analysis of the model demonstrated that the stability of the food web is controlled solely
by the two stabilizing terms: carrying capacity and
predation. As demonstrated for other simple food webs
(Visser et al. 2012), it can be shown that also for this system
the adaptive trait (k . 0) promotes coexistence and
asymptotic stability in a large parameter space.
Seasonal dynamics—We examine the model ecosystem in
an idealized zero-dimensional setting. Starting from the
arbitrarily low initial conditions, the system represented in
Eq. 2 reaches repeating annual cycles of abundance after
1 yr (Fig. 3), and we consider only subsequent years in the
following. The simulated seasonal dynamics of the plankton community are consistent with the classical pattern
observed in temperate oceans; a distinct maximum phytoplankton abundance in spring dominated by nonmotile
phytoplankton (diatoms, or Rn ), with a subsequent increase of motile phytoplankton during summer and early
autumn (flagellates, or Rm; Fig. 3a). Zooplankton abundance (C) is low during winter and increases in spring, with
a maximum in summer (Fig. 3b).
When compared with observed time series of diatoms and
dinoflagellates (Fig. 4), we note that the model reproduces the
general shape of the seasonal cycle and approximate
maximum biomass for both motile and nonmotile phytoplankton, while overestimating their minimum concentrations
(Fig. 4a,b). Moreover, the predicted grazer abundances (0–
14,000 ind. m23) are of a similar order of magnitude as
zooplankton abundances observed in temperate oceans (Eloire
et al. 2010). Hence, the model captures some aspects of real
plankton communities despite its simplified structure and
idealization of important processes of plankton ecology.
Although the two phytoplankton populations in the
model have the same growth rate, Rn alone sustains the
178
Mariani et al.
that of the phytoplankton, the grazer population has a
lagged response to prey abundances, maintaining the
competitive advantage of nonmotile phytoplankton over
motile plankton until e reduces, yielding ba , bc. The
phytoplankton uptake rate contributes to maintaining the
decoupling between phytoplankton and grazers. In our
model, we assume first-order kinetics for both uptake and
predation dynamics, thus neglecting saturating effects,
which can potentially alter the delayed grazer response to
phytoplankton biomass increase. Notably, species abundances tend to follow the fixed point throughout the year,
but less so in winter and when the spring bloom occurs. As
previously suggested (Evans and Parslow 1985), the bloom
formation in this system is a deviation from the general
quasi-equilibrium behavior of the model.
The results above are quite similar when the model is
applied in the vertical column setup (Fig. 5). In early spring,
the phytoplankton community is dominated by nonmotile
species (Rn, Fig. 5a) and abundances start increasing when the
column is still well mixed. Rn reaches its maximum at the
beginning of the stratification (day 90) in the surface layers
(Rn < 300 mg C m23 at depth , 35 m). Later, stratification of
the water column reduces e at depth (. 25 m) favoring the
increase of motile species (Rm, Fig. 5b), but also the increase
of grazer biomass (C, Fig. 5c). Feeding strategies are highly
variable close to the surface in summer, whereas ambush
feeding is favored at 20–50 m (t, Fig. 5d). Feeding-current
feeding (t 5 1) is dominant in winter and early spring when
the concentration of grazers is low (Fig. 5c,d). The deep
phytoplankton maximum dominated by motile cells is
established after the spring bloom at ca. 30 m depth and
deepens during summer until autumn. In autumn, mixing and
limitation of light decrease Rm to minimum values; in winter
an equilibrium is reached between phytoplankton species with
Rn . Rm. The abundance of zooplankton starts increasing in
spring (day 70), is at a maximum in midsummer, but reduces
to lower values in late autumn. Zooplankton abundance is
uniform in the upper 20 m but declines at depth.
Fig. 2. Concentrations of (a) phytoplankton, (b) grazers, and
(c) magnitude of the behavioral trait at the fixed point. Rm , Rn ,
and t* are functions of turbulence, whereas C* is function of
turbulence and carrying capacity.
increase in biomass around day 110. Thus, rather than
reflecting changes in K and I (Sverdrup 1953), this effect in
our model is driven by predation. The increase of
turbulence at the end of summer enhances the feeding rate
on motile species, yielding Rn . Rm (around day 250), a
condition that holds until the next spring. During spring,
the zooplankton feed mainly on nonmotile phytoplankton
because this is the most abundant prey (Fig. 3c). However,
because the growth rate of the zooplankton is slower than
Sensitivity to the parameters—The sensitivity of model
predictions to the choice of parameter values was tested
using summer conditions of I and e and calculating the
concentrations at the fixed point for changing parameter
values. The model outcomes are generally robust to
changes in parameter values but are particularly sensitive
to changes affecting the encounter rates (Table 1). In
particular, the effects of predation (p), conversion efficiency
(c), and encounter radius on nonmotile (a2) and motile (a1)
phytoplankton are shown in Fig. 6.
When no behavior-dependent mortality is prescribed in
the model (p 5 0), the motile species dominates over
nonmotile species because bc . ba in summer (Fig. 6a).
However with p 5 0 the model will produce a larger spring
increase of Rm over Rn (data not shown). Increasing p
reduces C* and increases Rn , whereas Rm is not affected
(Fig. 6a). On the other hand, increasing c affects all three
species: C* increases and Rm and Rn decrease proportionally. It is worth noting that changes in c, which describes
the simulated cell size, are not affecting the results for the
phytoplankton community structure.
Grazing behavior and plankton community
179
Fig. 3. Seasonal dynamics of (a) nonmotile (Rn, gray) and motile phytoplankton (Rm, black),
(b) grazers (C), and (c) the behavioral trait t. Also shown are the values at the fixed point of the four
state variables Rm , Rn , C*, and t* (dashed lines). In panel (c), the gray line shows the value of the
behavioral trait (tratio) obtained with a different formulation of fitness (i.e., g[t] 5 r[t]/d[t]).
The parameters with the largest effects are the encounter
radii (a1,2), which determine phytoplankton community
structure and grazer feeding behavior (Fig. 6c,d). Phytoplankton biomass is particularly sensitive to changes in the
encounter radius; that is, a change of 30% in this value
produces . 40% change in the relative biomass of one
phytoplankton species. This is expected from the quadratic
form, in which encounter radius appears in the feeding
interactions with motile and nonmotile species. Variation
among grazer species in hydrodynamic sensitivity and,
hence, perception distances to phytoplankton prey, are
likely to be of this magnitude, but phytoplankton species
composition, biomasses, and phenology show similarly
high variability.
However, the predicted seasonal change in the relative
significance of motile and nonmotile is robust to changes of
parameters because the summer concentrations are controlled by the relative values of the fixed point (Fig. 2a).
180
Mariani et al.
growth, mortality, predation, and adaptive grazing. Community dynamics are set not only by what is physically
possible but also what is best in terms of fitness trade-offs for
the myriad of individual organisms that make up the
ecosystem (Margalef 1998). The ubiquitous actions of
nonlinear and local interactions among a large number of
biological and physical components result in the emergence
(Levin 2005) of a marine food web within which trophic
interactions take place in an ever changing setting. In pelagic
ecosystems, light, nutrient availability, and turbulence are
normally considered the major factors affecting the structure
and function of the plankton community (Margalef 1978;
Huisman et al. 1999, 2004), whereas the role of predation by
zooplankton has received much less attention. However, we
have demonstrated using a simple community model that
adaptive zooplankton grazing behavior can promote coexistence among motile and nonmotile phytoplankton groups
and drive a seasonal succession from nonmotile to motile
forms. Additionally, adaptive grazing behavior enhances the
stability of the model food web.
Fig. 4. Average seasonal cycle of (a) modeled biomass of Rn
(white) and Rm (black) shown as monthly averages (bars) and
daily values (dark line, motile; gray line, nonmotile species); (b, c)
diatoms (white bars) and dinoflagellates (dark bars) from (b)
biomass data from a station near Stonehaven, Scotland
(56u57.89N, 02u06.29W), averaged over 1997–2006 and (c)
abundance data from the Continuous Plankton Recorder (CPR)
survey in the entire North Atlantic survey area, averaged over
1958–2006. In panel (a), the maximum peak of the daily plot of
nonmotile species occurring at , 600 mg C m23 is not shown. In
panel (c), the dinoflagellates (dinofl.) exclude heterotrophic taxa
but include photoautotrophs and mixotrophs.
Finally, it is interesting to note that when an alternative
formulation of fitness is used in the model (i.e., g[t] 5 r[t]/
d[t]), the results for the seasonal dynamic of the three
species are the same, and the only difference that can be
distinguished is for t, which has oscillations with slightly
smaller amplitudes during summer and relative higher
values during winter (Fig. 3c).
Discussion
General—In the pelagic ocean, plankton community dynamics are governed by a complex interaction between
physical and biological processes. Physical variables such as
light, temperature, turbulence, and upwelling have a direct
effect on the marine ecosystem. Superimposed on the
physical environment are biological processes, such as
Seasonal cycle—The model reproduces characteristic
features of the seasonal phytoplankton and zooplankton
succession that are well documented in temperate oceans:
(1) a distinct, short spring phytoplankton increase, (2) the
seasonal variation in the relative abundance of motile and
nonmotile phytoplankton (Margalef 1978; Cullen et al.
2002), (3) a deep phytoplankton maximum dominated by
motile forms during summer, and (4) the seasonal variation
in abundance of grazers with highest biomass during
summer (Kiørboe 2008). We in particular emphasize the
predicted seasonal successions of the phytoplankton from
nonmotile to motile forms: this is a consistent feature of
phytoplankton succession in temperate oceans and transcends variations in species composition (Margalef 1978).
In our model, it is solely the result of the adaptive grazing
behavior and is thus generated by processes entirely
different from those that are normally considered to govern
phytoplankton succession (turbulence, nutrients). Phytoplankton development is sustained by an increase in light
availability during spring, and it is mainly composed of
nonmotile phytoplankton. Dominance of nonmotile species
in spring is a result of their higher abundance in winter.
This is governed by grazing pressure that in autumn tends
to be higher on motile species. In winter, grazer abundance
is too low to control the nonmotile biomass. This pattern is
supported by a recent analysis of bloom formation in the
North Atlantic Ocean (Behrenfeld 2010) that found an
important role for grazing in controlling the phytoplankton
seasonal cycle. It is the seasonally varying balance between
phytoplankton growth and grazing that controls bloom
development (Evans and Parslow 1985; Irigoien et al. 2005;
Behrenfeld 2010) and possibly the community structure of
phytoplankton. However, in our model, the nonsaturating
formulation of the feeding rates can likely overestimate the
grazing pressure during the bloom phase, thus affecting the
extent of the bloom period.
Grazing process—One model prediction in particular is
counterintuitive and in apparent conflict with experimental
Grazing behavior and plankton community
181
Fig. 5. Seasonal dynamic of (a) Rn, (b) Rm, (c) C, and (d) behavioral trait t from the
simulations with the coupled one-dimensional model. The results are for the stationary limit cycle
reached by the model at year 7 after starting from uniformly low initial concentrations. (d) As
reference, the black line indicates the edge of grazer concentration C 5 15 mg C m23.
observations: that feeding-current behavior is favored
under more turbulent conditions and ambush behavior
under less turbulent conditions. Theory and experiments
both suggest that prey encounter rates are significantly
enhanced by moderate levels of turbulence in ambushfeeding grazers but not in feeding-current feeding ones
(Kiørboe and Saiz 1995; Saiz and Kiørboe 1995). Moreover, copepods can switch between the two feeding
behaviors, adopting the most rewarding feeding behavior
(Kiørboe et al. 1996). This apparent discrepancy between
model and observations is due to grazing interactions and
population dynamics: in situations where ambush feeding
would be most favorable, the abundance of motile cells is
reduced to the extent that feeding-current feeding becomes
more rewarding and vice versa. This dynamic aspect of
grazer interactions is not easily reproduced in laboratory
experiments and, therefore, often not considered.
Our results and a growing appreciation for the importance of grazing in shaping plankton communities (Armstrong 1994; Behrenfeld 2010) provide a complementary
view to the classic bottom-up paradigm, which considers
competing phytoplankton species with different growth,
swimming, and sinking rates but all with an equal grazing
term. We suggest that trophic interactions, in particular
adaptive feeding behavior of zooplankton grazers, might be
important for structuring plankton communities. Additionally, the model predicts that there should be vertical
gradients in the relative significance of the two feeding
modes.
Limitations of the model—The model we have analyzed is
highly idealized and disregards a number of processes
thought to affect phytoplankton community structure. In
particular, the model does not include some processes often
considered key in explaining the seasonal variation in
phytoplankton community structure, viz. trade-offs in
phytoplankton nutrient competition (Huisman et al. 1999;
Litchman et al. 2007), and phytoplankton mortality due
to sinking (Huisman et al. 2002). This simplification is
deliberate because it focuses attention on the effects of
trophic interactions, their modulation by environmental
factors (turbulence and light) and adaptive behavior, in
shaping phytoplankton communities. However, the differential grazing effect in our model might be overestimated
with respect to motility as a trait. Other properties of the
prey, such as cell size or ‘‘quality’’ (i.e., stoichiometry), are
known to influence grazing preferences of copepods
(Kiørboe 2008). These properties correlate both positively
182
Mariani et al.
Fig. 6. Summer values of Rn (light gray) Rm (dark gray), and C* (black) as function of (a)
predation risk (p), (b) conversion efficiency (c), and (c) reaction distance to nonmotile prey (a2)
and (d) motile prey (a1). Dot symbols indicate the parameter values used in the model.
as well as negatively with motility, depending on the
current species composition. Although such additional
processes can be included in the model, increasing model
complexity comes at the cost of increasing the number of
parameters. Additional, detailed modeling analyses exploring different plankton traits and their trade-offs, along with
adaptive grazing behaviors, are interesting directions that
can be addressed in future.
We have considered a generalist grazer that can switch
between feeding in either of two modes, and we have been
able to make a quantitative analysis because the trade-offs
between the two feeding modes are known. In nature,
however, there are specialist grazers that are obligate ambush
or feeding current feeders, and their feeding behavior is not
adaptive. To supplement the model with specialist feeders
requires knowledge also of the trade-offs between being a
generalist and a specialist for the two feeding modes. We can
hypothesize that the specialists are better at their métier than
the generalists in terms of higher encounter rates and lower
mortality rates. However, we are presently unable to quantify
these trade-offs. Quantification could be achieved from a
reanalysis of, for example, the encounter rates of the two
feeding modes (Kiørboe 2011), wherein the organisms are
divided between specialists and generalists.
Modeling implications—Laboratory and direct observations suggest that copepod feeding behaviors can adapt to
changing local environmental conditions. Plasticity in
behavior implies changes in copepod vital rates, such as
feeding and mortality rates (Mariani and Visser 2010). We
have shown that when behaviorally driven changes in vital
rates are introduced in a simple population model, several
features of the plankton community can be reproduced.
We do not contend that this model is a fully realistic
description of plankton communities because the model
does not resolve many processes that are important in
plankton dynamic. For example, we do not explicitly resolve
the sinking of cells, which could be responsible for the
overestimate of winter concentrations of diatoms (Fig. 5).
Similarly, a more detailed description of the nutrient uptake
dynamics could promote a competitive advantage for
dinoflagellates in summer. On the other hand, the simplicity
of the model makes the interpretation of the results easier
than more complex models of plankton dynamics, which
typically include many parameters and variables. Using this
simple model, we are able to demonstrate that fitnessoptimizing adaptive responses of grazers’ foraging behavior
can promote seasonal changes in plankton community. We
suggest that more comprehensive, global models of marine
ecosystems should account for behavioral changes and
adaptation of zooplankton (Follows et al. 2007).
It has been suggested that behavioral control of zooplankton feeding on multiple resources can be heuristically
described using several classes of switching functional
Grazing behavior and plankton community
responses (Gentleman et al. 2003) and that subtle changes in
the functional response can produce remarkable differences
in species distribution and abundances simulated by complex
ecosystem models (Anderson et al. 2010). Although a
systematic comparison between our approach and switching
functional responses is outside the scope of our paper, we
note that our approach is consistent with an active switching
functional response (Gentleman et al. 2003). Indeed, the fixed
point t* is equivalent to the standard parameterization of
constant predator preference on multiple resources (Gentleman et al. 2003). However, using t* in the integration of Eq.
2, the two resources have a neutral dynamic, and the model
would produce no changes in phytoplankton community
under seasonal forcing. Our model description of varying
predator preference (Eq. 4) differs from a simple switching
function because it depends not only on relative abundances
but also the other factors influencing grazer fitness (turbulence, light, and predation). The emergent community
structure of the modeled system arises as much through
fitness-optimizing behavior of grazers as it does through
population dynamics. This property of the model is based
upon a mechanistic description of the encounter process
(with both predator and prey) and on observed adaptive
feeding behavior in zooplankton.
Acknowledgments
We are grateful to Jens Rasmussen and Eileen Bresnan as well
as the Sir Alister Hardy Foundation for Ocean Science for the
data in Fig. 4b. Thanks also to Chris Klausmeier for discussions
during the revision of the paper. The authors also thank the
reviewers and the editor R.W. Sterner for their valuable comments
during the manuscript review process.
This work was supported by a Danish Research Council grant
(272-07-0485). P.M. was supported by the projects: ‘‘Sustainable
fisheries, climate change and the North Sea ecosystem’’ (SUNFISH, Danish agency for Science, Technology and Innovation)
and ‘‘Towards coast to coast networks of marine protected areas’’
(COCONET, EU FP7 Grant Agreement 287844). A.D.B. was
supported by the Gordon and Betty Moore Foundation’s Marine
Microbiology Initiative.
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Received: 05 January 2012
Accepted: 21 July 2012
Amended: 14 September 2012