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Photochemistry and Photobiology, 2006, 82: 903–908
Symposium-in-Print: UV Effects on Aquatic and Coastal Ecosystems
The Whole Is More Than the Sum of Its Parts: Modeling
Community-Level Effects of UVR in Marine Ecosystems
Fernando Momo*1, Emma Ferrero2, Matıas Eory2, Marisol Esusy2, Julia Iribarren2,
´ ¨
Gustavo Ferreyra3,5, Irene Schloss3,4, Behzad Mostajir5 and Serge Demers5
1
Universidad Nacional de General Sarmiento, Instituto de Ciencias, Los Polvorines, Argentina
2
´ ´ ´
Universidad Nacional de Lujan, Departamento de Ciencias Basicas, Lujan, Argentina
3
´
Instituto Antartico Argentino, Buenos Aires, Argentina
4
CONICET, Ciudad de Buenos Aires, Argentina
5
´ ´ ´
Universite du Quebec, Institut des sciences de la mer de Rimouski, Rimouski, Quebec, Canada
Received 30 September 2005; accepted 17 April 2006; published online 18 April 2006 DOI: 10.1562/2005-09-30-RA-706
radiation (PAR, 400–700 nm) (1). Although ozone depletion is
ABSTRACT
stronger at high latitudes, there are ozone losses over other regions
The effect of UVB radiation (UVBR, 290–320 nm) on the (2,3) and we must consider the UVBR enhancement as a global
dynamics of the lower levels of the marine plankton com- problem that can affect aquatic and terrestrial communities.
munity was modeled. The model was built using differential Although solar UVBR is rapidly attenuated within the water
equations and shows a good fit to experimental data collected column, it can in some instances penetrate at biologically sig-
in mesocosms (defined as large enclosures of 1500 L filled with nificant radiation levels down to approximately half of the euphotic
natural marine waters). Some unexpected results appear to be zone (1,4). On a broader ecological scale UVBR is known to be the
possible by indirect effects in prey (bacteria, phytoplankton most harmful waveband of solar UVR for aquatic organisms, as
and heterotrophic flagellates). In particular, apparent compe- well as for whole ecosystems (5–7).
tition appears between small phytoplankton and bacteria. It is accepted that UVBR affects all components of pelagic
This effect is caused by a shared predator (ciliates). Another communities, from bacteria to fish. UVBR effects on phytoplank-
remarkable effect is an increase in bacteria and flagellates ton and bacteria, which are the base of the aquatic food web, have
populations due to enhanced UVBR. This effect is similar to been intensely studied. Adverse effects on phytoplankton can
that observed under mesocosm experimental conditions and is inhibit photosynthesis (8,9), alter their nutrient uptake (10,11), lead
related to the decrease of predation due to the direct damage to changes in pigment composition (12), induce damages to DNA
to predators (ciliates) by UVBR. The effect of UVBR changing (13) and increase cell size (14). At the community level UVBR can
interaction coefficients may be dramatic on the community alter species composition and interspecific interactions (15,16),
structure, producing big changes in equilibrium populations, with consequences for the upper levels of the planktonic food web
as demonstrated by sensitivity analysis of the model. In order dynamics (7,14,17).
to generalize these results to field conditions it will be nec- As a consequence synthetic parameters at the community level,
essary to increase model complexity and include extra organic such as species diversity, must be affected by UVBR. However,
mater sources, mixing and sinking effects and predation by there are only few studies focusing on whole communities, includ-
large zooplankton. This work shows that UVBR may produce ing interactions among species (18). Furthermore, mesocosms
community global responses that are consequence of both studies presented in this special issue and in other publications
direct and indirect effects among populations. show complex and nontrivial changes in planktonic community
structure at different latitudes and support the idea that UVBR
alters predator-prey relationships, forcing paradoxical changes in
INTRODUCTION phytoplankton populations (19–21).
Mathematical models are useful tools that can help us to explore
Stratospheric ozone depletion occurring over Antarctica during the
long-term consequences of UVBR-induced changes and to simu-
austral spring (known as the ‘‘ozone hole’’) increases the exposure
late new ‘‘scenarios’’ considering different doses. In this article we
of high-latitude plankton communities to UVB radiation (UVBR,
develop some general criteria useful to build plausible mathemat-
280–320 nm). There is striking evidence that ozone depletion alters
ical models of UVBR effects in planktonic communities. We first
the solar spectral balance by changing the ratio of UVBR to UVA
construct a conceptual model for the community under study (i.e.
radiation (UVAR, 320–400 nm) and photosynthetically available
mesocosm experiments). Second, we formulate the model mathe-
matically and then simplify and analyze it. Third, we fit the model
to data obtained under natural UVBR conditions. Fourth, we
*Corresponding author email: fmomo@ungs.edu.ar (Fernando Momo)
simulate a UVBR increment and analyze its consequences. A brief
Ó 2006 American Society for Photobiology 0031-8655/06
903
904 Fernando Momo et al.
are considered to be self-limiting (that is, with logistic dynamics) and the
other compartments are expressed by exponential equations.
To perform the sensitivity analysis, we varied each parameter, one at
a time, in a fixed proportion (10%), thus computing the variation of each
variable as a percentage of its anterior values. In these analyses the signs of
the parameter and variable were taken into account in order to establish the
type of control that the parameter has on the variable.
RESULTS
The model
The coupling between phytoplankton and bacteria is given by
excretion rates (exi); this relationship implicitly includes DOC.
In the same way, mortality rates (mi) implicitly include POC.
Consequently, only five equations remain in the model, which has
the following form:
Figure 1. Conceptual model of plankton relationships in mesocosm
experiments. Black arrows indicate negative effects of UV-B.
dFc
¼ FcðA1 À B1 Fc À m1 À ex1 À p1 CÞ
dt
dFg
¼ Fg ðA2 À B2 Fg À m2 À ex2 Þ
discussion about how to generalize this type of model to open dt
dB
water conditions is also presented.
¼ Bðe1 ðex1 Fc þ ex2 Fg Þ À m3 À p3 CÞ
dt
dC
¼ Cðe3 p2 Fh þ e4 p3 B þ e5 p1 Fc À m4 Þ
dt
MATERIALS AND METHODS dFh
¼ Fhðe2 m3 B À p2 C À m5 Þ
Experimental data. The data used to fit the model are based on mesocosm dt
experiments performed on the southern shore of the lower St. Lawrence
Estuary (Quebec, Canada; lat 48.68N, long 68.28W) during July 1996 (22).
A time-series experiment was carried out for 7 days, using eight land-based Each equation represents the rate of change of each biological
mesocosms (2.25 m depth) that each contained 1500 L of St. Lawrence
compartment, expressed as an algebraic sum of inputs and outputs.
Estuary surface water previously passed through a 240 lm Nitex screen.
Table 1 gives the definition and units of the different parameters
Pairs of mesocosms were submitted to four UVB treatments: natural UVBR
and a set of possible values obtained after fitting the model to data
as control, low UVBR enhancement, high UVBR enhancement and no
UVBR. The UVB intensities were increased using lamps. In the fourth from the natural UVBR treatment. We fitted the model to data from
treatment natural UVB radiation was removed by a 0.13 mm Mylar D sheet.
(22), obtaining good results (Fig. 2). A first look shows that the
Dynamics of ciliates (length, 15–35 lm), heterotrophic flagellates (2–10
model can be considered a reasonable representation of the
lm), heterotrophic bacteria (,1 lm), small phytoplankton (,5 lm) and
real system. The fitting was performed by maximum likelihood
large phytoplankton (5–20 lm) were monitored during the experiment. To
fit our model we used data corresponding to the first treatment (natural regression analysis, using parameters without constraints and mini-
UVBR) and then we simulated an enhancement of UVBR by means of an mizing the quadratic differences between predicted and observed
increase its possible effects, as explained below.
values for each biological variable. Figure 2 shows the fit for small
Model construction and sensitivity analysis. To build a mathematical
phytoplankton (Fig. 2a), large phytoplankton (Fig. 2b), heterotro-
model, we must have a clear picture of the biological problem to be studied.
phic flagellates (Fig. 2c) and bacteria (Fig. 2d). The model approx-
In this case, mesocosm experiments were carried out using a simplified
community, constituted only by phytoplankton, bacteria (B) and small imates data very well for all variables with the exception of
zooplankton; mesozooplankton, similar to microcrustaceans, were excluded
bacteria. In this case the model exhibits a more fluctuating dynamic
by prefiltration. After experimental observations, the model considered
than the real data (Fig. 2d).
two phytoplankton fractions: small phytoplankton (Fc; cells 1–5 lm long)
A closer look at the model shows that the large phytoplankton
and large phytoplankton (Fg; cells 5–20 lm long). Zooplankton was
also subdivided in two fractions: ciliates (C) and heterotrophic flagellates (Fg) is autonomous (i.e. it does not depend on other compartments)
(Fh). and its equilibrium point is given by Fg* 5 (A2 À m2 À ex2)/B2.
We considered a conceptual model with two additional compartments
This compartment is a donor but it has no controllers. The system
connecting biological boxes: detritic particulate organic carbon (POC) and
can be reduced again, this time to four equations:
dissolved organic carbon (DOC). However, these two boxes were not
included in the mathematical formulation, as explained below. Figure 1
represents the conceptual model; each box is a variable, thin arrows
represent fluxes and wide arrows represent possible deleterious effects dFc
¼ FcðA1 À B1 Fc À m1 À ex1 À p1 CÞ
of UVBR.
dt
This system involves seven compartments and is expressed by a very
dB
complex set of equations that may become untreatable from a mathematical ¼ Bðe1 ex1 Fc À m3 À p3 CÞ
dt
point of view. Fortunately, we can simplify the problem and reduce its
dC
dimensionality by eliminating the two organic carbon boxes and shifting
¼ Cðe3 p2 Fh þ e4 p3 B þ e5 p1 Fc À m4 Þ
them to an implicit form. The mortality of bacteria is directly linked to dt
feeding by heterotrophic flagellates; similarly, the excretion rate of small
dFh
phytoplankton is linked directly to bacteria nutrition. Moreover, we can ¼ Fhðe2 m3 B À p2 C À m5 Þ
dt
simplify the dynamic system as follows: only the phytoplankton fractions
Photochemistry and Photobiology, 2006, 82 905
Table 1. Mean of each parameter in the model, units and values obtained
fitting the model to experimental data (19) without UVR addition.
Symbol Definition Units Fitted value*
DayÀ1
A1 Intrinsic rate of increase of 1.6
small phytoplankton
L dayÀ1 cellsÀ1
B1 Self-limiting term of small 5 E-5
phytoplankton in the
logistic equation
dayÀ1
m1 Mortality rate of small 0.02
phytoplankton
dayÀ1
ex1 Excretion rate of small 0.001
phytoplankton
(producing DOC)
dayÀ1 cellsÀ1
p1 Rate of predation of small 6 E-4
phytoplankton by ciliates
À1
A2 Intrinsic rate of increase of day 0.3
large phytoplankton
L dayÀ1 cellsÀ1
B2 Self-limiting term of large 5.08 E-7
phytoplankton in the
logistic equation
dayÀ1
m2 Mortality rate of large 3 E-4
phytoplankton
dayÀ1
ex2 Excretion rate of large 0.02
phytoplankton
(producing DOC)
e1 Efficiency of DOC Nondimensional 0.006
assimilation by bacteria
dayÀ1
m3 Mortality rate of bacteria 0.003
dayÀ1 cellsÀ1
p3 Rate of predation of bacteria 0.009
by ciliates
e3 Efficiency of heterotrophic Nondimensional 4.3 E-4
flagellates conversion by
ciliates
dayÀ1 cellsÀ1
p2 Rate of predation of 5 E-5
heterotrophic flagellates
by ciliates
e4 Efficiency of bacteria Nondimensional 9 E-5
conversion by ciliates
e5 Efficiency of small Nondimensional 0.001
phytoplankton assimilation
by ciliates
dayÀ1
m4 Mortality rate of ciliates 0.6
dayÀ1
m5 Mortality rate of 0.005
heterotrophic flagellates
cellsÀ1
e2 Efficiency of heterotrophic 3 E-5
flagellates assimilation
eating dead bacteria
*E-4 5 310À4, E-5 5 310À5, and so on.
Finding the four population equilibria, we verify that there is
only one condition of coexistence for the four populations. This
condition is given by:
p3 ðA1 À m1 À ex1 Þ À m3 p1
*
Fc ¼
Figure 2. Model fitted to experimental data of natural UVBR treatments;
ex1 e1 p1 þ p3 B1
small phytoplankton (Fc) (a), large phytoplankton (Fg) (b), heterotrophic
ex1 e1 p2 ðA1 À m1 À ex1 Þ þ B1 ðp3 m5 À p2 m3 Þ þ m5 ex1 e1 p1 flagellates (Fh) (c) and bacteria (B) (d).
B* ¼
e2 m3 ðex1 e1 p1 þ p3 B1 Þ
ex1 e1 ðA1 À m1 À ex1 Þ À B1 m3
Under natural UVBR conditions there is an indirect effect
C* ¼
ex1 e1 p1 þ p3 B1 between the three types of prey eaten by ciliates: bacteria, small
Fh* ¼ f½e4 e1 ex1 p2 p3 ðA1 À m1 À ex1 Þ phytoplankton and heterotrophic flagellates. This effect can be
þ e5 p1 e2 m3 ðp3 A1 þ p1 m3 À p3 m1 À p3 ex1 Þ understood in two ways. The first interpretation is to consider a
top-down effect by which the ciliates regulate their three prey. If
À e4 p3 ðm3 p2 B1 À m5 ex1 e1 p1 À p3 m5 B1 Þ
true, any increase in the population of one type of prey should be
À m4 e2 m3 ðex1 e1 p1 þ p3 B1 Þ=
a consequence of the predator’s preference for another type of prey.
½e3 p2 e2 m3 ðex1 e1 p1 þ p3 B1 Þg The second possibility is a regulation that combines bottom-up and
906 Fernando Momo et al.
Sensitivity analysis
In order to clarify the results, we performed a sensitivity analysis in
which one parameter at a time was varied in a fixed proportion and
we measured the output variation in each variable. The results are
shown in Fig. 4.
Considering only the higher sensitivities (a 10% variation in the
parameter produces a minimum variation of 5% in the output),
we can see that Fc is a self-controlled variable: the significant
sensitivities are for its own growth parameters (A1 and B1) (Fig.
4a). In the case of ciliates the control factors are related to the
growth efficiency of the most abundant prey (bacteria) (i.e. ex1 and
e1) and with the dynamics of one secondary prey (small phyto-
plankton) (i.e. A1 and B1) (Fig. 4b). As a consequence there is
a bottom-up control of ciliates.
As we can see in Fig. 4c heterotrophic flagellates are controlled
both by predators (ciliates) and by prey (bacteria), because the
variable Fh is sensitive to p3 and e4 (the parameters that regulate
the predation of ciliates over bacteria) and to e2 (the transformation
efficiency when eating bacteria). As a consequence heterotrophic
flagellates have one bottom-up and three top-down controls.
Finally, bacteria are totally controlled by the predator ciliate
because bacteria are mainly sensitive to p3, e4 and m4 (Fig. 4d); the
first two are predation parameters and the third is the predator
mortality rate.
Analysis of the equilibrium expression reveals that a small
phytoplankton population will increase if the predation on bacteria
is higher (p3 increases), the mortality of bacteria increases (m3) or
the term B1 decreases (less self-competition). The first effect (an
Figure 3. Effect of increase mortality rates (increment of 10%) in increase of small phytoplankton population when p3 increases) is
all compartments simulating UVBR effects in bacteria (a) and hetero- given for a sort of ‘‘preference’’ of the predator for bacteria; this
trophic flagellates (b). NUV 5 natural UVBR dose, UV 5 UVBR
preference is given by a higher efficiency of capture ( p3). The
enhanced 10%.
second effect (an increase in small phytoplankton population when
m3 increases) may represent an indirect effect: if bacteria mortality
top-down effects. In this case, growth in one prey causes a predator is higher, heterotrophic flagellates have more food and their
population increase (bottom-up effect) and the enhancement of population grows; ciliates are offered more flagellates and eat less
predation pressure on the other prey types produces a diminution in on Fc. The third effect (small phytoplankton equilibrium increases
this prey population (top-down effect). In the latter case the growth when B1 decreases) is a simple self-competition effect. All these
of one of the prey compartments produces the decrease of the other effects are deducible from the equilibrium point expression.
two by improving the predator (C) population. This kind of effect Ciliates benefit from a slight increment in the mortality rate of
is called ‘‘apparent competition’’ (23,24): there is no competition bacteria (m3) because Fc and Fh increase and there is more prey
for resources but the population dynamics mimic the competition biomass for ciliates. Therefore, ciliates eat more phytoplankton and
dynamics because each increase the population of one type of prey heterotrophic flagellates and bacteria can grow again. Another
produces a decrease in the other two prey populations. The interesting result is the counterintuitive effect of p3 (the predation
mathematical expressions for equilibrium suggest that this last efficiency over bacteria): when ciliates have high efficiency, their
interpretation may be the correct one. equilibrium biomass is lower, which indicates that, for ciliates, it is
an advantage to be a ‘‘prudent’’ predator sensu (25).
The effect of UVBR
We simulated the UVR effects as an increment of 10% in all
DISCUSSION
mortality rates. This approach is not perfect because different
organisms have different sensitivities to UVR and show different The importance of bacteria and bacterivory is well established
remediation capacities. On the other hand, it is necessary to (19,26). Heterotrophic bacteria use dissolved organic matter to
emphasize that these mortality rates are really the expression of build up their cellular material and the newly formed bacterial
a net effect between damage and repair in each biological com- biomass is transferred to metazoans via protozoan bacterivory
partment. Despite these limitations we consider that our approx- (mainly heterotrophic ciliates). Our results show that, under simple
imation is roughly correct because we can model changes that assumptions, the dynamics of a planktonic system with phyto-
closely match field observations: bacteria benefit from UVBR plankton, bacteria and protozoa can be simulated and studied.
because of a decrease in the ciliate predation (Fig. 3a) and the same Protozoan bacterivory may be considered a key process in
effect is evident for heterotrophic flagellates (Fig. 3b). Small and recovering a considerable part of the primary production that
large phytoplankton were not affected by the UVBR increase in would otherwise be lost to aquatic food webs and is believed
the model. to indirectly impact carbon flux dynamics by regulating standing
Photochemistry and Photobiology, 2006, 82 907
stocks, species composition and metabolic activity of the bacterial
community. In our model it is evident that ciliates regulate bacteria,
heterotrophic flagellates and small phytoplankton populations
and that this dynamic can cause surprising results via indirect
interactions, such as the apparent competition between bacteria and
small phytoplankton that have a common predator (24).
A major problem of contemporary science is to understand the
structure and dynamics of complex systems. In particular, the
model presented here is focused on the response of the whole
community to UVBR stress and it emphasizes the importance of
biological interactions in determining that response. Our model is
capable of simulating the community response to UVBR. When
a UVR increase is simulated by adding the same percentage of
mortality to all biological compartments, bacteria, heterotrophic
flagellates and small phytoplankton benefit from the relaxation of
predation pressure. This result coincides with field and experi-
mental observations (22). It is clear that UVR can affect the
bacterivory by protozoa; for instance, a loss of motility and,
consequently, a decrease of the bacterivory of the heterotrophic
nanoflagellates after their exposure to UVB has been reported
(17,22). However, we demonstrate that a prey increase is not
necessary the result of a differential damage between prey and
predators; in fact, the coexistence equilibrium is moved toward
a situation with more prey and less predators simply by introducing
the same increase in mortality rates for both populations Although
this result is similar to the found in the most classic work in
predation (27), it is probably the most important topic to take into
account in the interpretation of experimental data and in the
prediction of future scenarios.
UVRB effects on communities may not be explained only by
differences in damage/repair ratios among species. Changes at the
community level are complex and characteristic of high levels of
organization. As demonstrated by the sensitivity analysis, small
changes in some parameters may produce dramatic alterations in
community composition at equilibrium. In particular, if UVBR
decreases predation coefficients ( p1, p2, p3), all of the populations
change and the whole community is driven to a new equilibrium
point.
Another modeling study found indirect effects in planktonic
communities (18). That model was similar to the one presented
here but the nutrients dynamics were explicitly included, showing
apparent mutualism among phytoplankton and bacteria. In our
model nutrients are not explicitly included and the main indirect
effect is an ‘‘apparent’’ competition between bacteria and small
phytoplankton due to predation.
The good fit with the data suggests that our formulation (without
nutrients) can be sufficient to analyze the global behavior of this
kind of community. We can assume that, in conditions of nutrient
depletion, the stronger indirect effect will be mutualism (18);
however, an increment in nutrients supply to nonlimiting con-
ditions will probably show apparent competition as the most
important effect. This effect is due to increased predator popu-
lations. This kind of variable interaction has been reported in the
ecological literature (28). Evidently, more studies are necessary in
Figure 4. Sensitivity analysis for the parameters in the short model. Bars
order to extend these kinds of models to field conditions. Although
show the percentage variation in the output produced by a 10% variation in
mesocosms can be considered better experimental models than
each parameter (in abscissa). Negative values indicate that an increment in
microcosms (Belzile et al., this issue), they do not include all the the parameter produces a decrease in the variable. Sensitivities of Fc (a),
physical effects that we find in the field, such as vertical mixing, sensitivities of C (b), sensitivities of Fh (c) and sensitivities of B (d).
the larger phytoplankton, the cascade effects produced by large
zooplankton (e.g. crustaceans or appendicularians) and the
dynamics of nutrients, DOC and POC. In particular, in field
908 Fernando Momo et al.
conditions there are DOC and POC inputs and outputs that must 10. Dohler, G. (1997) Effect of UVB radiation on utilization of inorganic
¨
nitrogen by Antarctic microalgae. Photochem Photobiol. 66, 831–836.
be considered to explain the observed patterns. Moreover, organic
11. Fauchot, J., M. Gosselin, M. Levasseur, B. Mostajir, C. Belzile,
matter interacts with UVR and increases its attenuation, and UVR
S. Demers, S. Roy and P. Villegas (2000) Influence of UV-B radiation
produces the photobleaching of DOC and POC (29,30). However, on nitrogen utilization by a natural assemblage of phytoplankton.
in the mesocosm experiments used to test the fit the model there J. Phycol. 36, 484–496.
12. Goes, J., N. Handa, S. Taguchi and T. Hama (1994) Effect of UV-B
were no extra sources of DOC or POC.
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Tetraselmis sp.: Relationship to cellular pigments. Mar. Ecol. Prog.
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13. Buma, A., E. Van Hannen, M. Veldhuis and W. Gieskes (1996) UVB
The model presented here shows a combination of very important radiation induces DNA-damage and DNA-synthesis delay in the
new results, which is very rewarding because of the simplicity of marine diatom Cyclotella sp. Sci. Mar. 60, 101–106.
14. Mostajir, B., T. Sime-Ngando, S. Demers, C. Belzile, S. Roy,
the model. It presents a very good fit with experimental obser-
M. Gosselin, J. Chanut, S. de Mora, J. Fauchot, F. Vidussi and
vations both under normal and UVBR-enhanced conditions. It
M. Levasseur (1999) Ecological implications of changes in cell size
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Acknowledgements—This work has been supported by an award from the
18. Aota, Y. and H. Nakajima (2000) Mathematical analysis on co-
Inter American Institute for Global Change Research (grant CRN-026).
existence conditions of phytoplankton and bacteria systems with
We thank Dr. Jose E. Ure for his assistance with solving some mathemat-
´
nutrient recycling. Ecol. Model. 135, 17–31.
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19. Chatila, K., S. Demers, B. Mostajir, M. Gosselin, J.-P. Chanut and
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Symposium-in-Print: UV Effects on Aquatic and Coastal Ecosystems
The Whole Is More Than the Sum of Its Parts: Modeling
Community-Level Effects of UVR in Marine Ecosystems
Fernando Momo*1, Emma Ferrero2, Matıas Eory2, Marisol Esusy2, Julia Iribarren2,
´ ¨
Gustavo Ferreyra3,5, Irene Schloss3,4, Behzad Mostajir5 and Serge Demers5
1
Universidad Nacional de General Sarmiento, Instituto de Ciencias, Los Polvorines, Argentina
2
´ ´ ´
Universidad Nacional de Lujan, Departamento de Ciencias Basicas, Lujan, Argentina
3
´
Instituto Antartico Argentino, Buenos Aires, Argentina
4
CONICET, Ciudad de Buenos Aires, Argentina
5
´ ´ ´
Universite du Quebec, Institut des sciences de la mer de Rimouski, Rimouski, Quebec, Canada
Received 30 September 2005; accepted 17 April 2006; published online 18 April 2006 DOI: 10.1562/2005-09-30-RA-706
radiation (PAR, 400–700 nm) (1). Although ozone depletion is
ABSTRACT
stronger at high latitudes, there are ozone losses over other regions
The effect of UVB radiation (UVBR, 290–320 nm) on the (2,3) and we must consider the UVBR enhancement as a global
dynamics of the lower levels of the marine plankton com- problem that can affect aquatic and terrestrial communities.
munity was modeled. The model was built using differential Although solar UVBR is rapidly attenuated within the water
equations and shows a good fit to experimental data collected column, it can in some instances penetrate at biologically sig-
in mesocosms (defined as large enclosures of 1500 L filled with nificant radiation levels down to approximately half of the euphotic
natural marine waters). Some unexpected results appear to be zone (1,4). On a broader ecological scale UVBR is known to be the
possible by indirect effects in prey (bacteria, phytoplankton most harmful waveband of solar UVR for aquatic organisms, as
and heterotrophic flagellates). In particular, apparent compe- well as for whole ecosystems (5–7).
tition appears between small phytoplankton and bacteria. It is accepted that UVBR affects all components of pelagic
This effect is caused by a shared predator (ciliates). Another communities, from bacteria to fish. UVBR effects on phytoplank-
remarkable effect is an increase in bacteria and flagellates ton and bacteria, which are the base of the aquatic food web, have
populations due to enhanced UVBR. This effect is similar to been intensely studied. Adverse effects on phytoplankton can
that observed under mesocosm experimental conditions and is inhibit photosynthesis (8,9), alter their nutrient uptake (10,11), lead
related to the decrease of predation due to the direct damage to changes in pigment composition (12), induce damages to DNA
to predators (ciliates) by UVBR. The effect of UVBR changing (13) and increase cell size (14). At the community level UVBR can
interaction coefficients may be dramatic on the community alter species composition and interspecific interactions (15,16),
structure, producing big changes in equilibrium populations, with consequences for the upper levels of the planktonic food web
as demonstrated by sensitivity analysis of the model. In order dynamics (7,14,17).
to generalize these results to field conditions it will be nec- As a consequence synthetic parameters at the community level,
essary to increase model complexity and include extra organic such as species diversity, must be affected by UVBR. However,
mater sources, mixing and sinking effects and predation by there are only few studies focusing on whole communities, includ-
large zooplankton. This work shows that UVBR may produce ing interactions among species (18). Furthermore, mesocosms
community global responses that are consequence of both studies presented in this special issue and in other publications
direct and indirect effects among populations. show complex and nontrivial changes in planktonic community
structure at different latitudes and support the idea that UVBR
alters predator-prey relationships, forcing paradoxical changes in
INTRODUCTION phytoplankton populations (19–21).
Mathematical models are useful tools that can help us to explore
Stratospheric ozone depletion occurring over Antarctica during the
long-term consequences of UVBR-induced changes and to simu-
austral spring (known as the ‘‘ozone hole’’) increases the exposure
late new ‘‘scenarios’’ considering different doses. In this article we
of high-latitude plankton communities to UVB radiation (UVBR,
develop some general criteria useful to build plausible mathemat-
280–320 nm). There is striking evidence that ozone depletion alters
ical models of UVBR effects in planktonic communities. We first
the solar spectral balance by changing the ratio of UVBR to UVA
construct a conceptual model for the community under study (i.e.
radiation (UVAR, 320–400 nm) and photosynthetically available
mesocosm experiments). Second, we formulate the model mathe-
matically and then simplify and analyze it. Third, we fit the model
to data obtained under natural UVBR conditions. Fourth, we
*Corresponding author email: fmomo@ungs.edu.ar (Fernando Momo)
simulate a UVBR increment and analyze its consequences. A brief
Ó 2006 American Society for Photobiology 0031-8655/06
903
904 Fernando Momo et al.
are considered to be self-limiting (that is, with logistic dynamics) and the
other compartments are expressed by exponential equations.
To perform the sensitivity analysis, we varied each parameter, one at
a time, in a fixed proportion (10%), thus computing the variation of each
variable as a percentage of its anterior values. In these analyses the signs of
the parameter and variable were taken into account in order to establish the
type of control that the parameter has on the variable.
RESULTS
The model
The coupling between phytoplankton and bacteria is given by
excretion rates (exi); this relationship implicitly includes DOC.
In the same way, mortality rates (mi) implicitly include POC.
Consequently, only five equations remain in the model, which has
the following form:
Figure 1. Conceptual model of plankton relationships in mesocosm
experiments. Black arrows indicate negative effects of UV-B.
dFc
¼ FcðA1 À B1 Fc À m1 À ex1 À p1 CÞ
dt
dFg
¼ Fg ðA2 À B2 Fg À m2 À ex2 Þ
discussion about how to generalize this type of model to open dt
dB
water conditions is also presented.
¼ Bðe1 ðex1 Fc þ ex2 Fg Þ À m3 À p3 CÞ
dt
dC
¼ Cðe3 p2 Fh þ e4 p3 B þ e5 p1 Fc À m4 Þ
dt
MATERIALS AND METHODS dFh
¼ Fhðe2 m3 B À p2 C À m5 Þ
Experimental data. The data used to fit the model are based on mesocosm dt
experiments performed on the southern shore of the lower St. Lawrence
Estuary (Quebec, Canada; lat 48.68N, long 68.28W) during July 1996 (22).
A time-series experiment was carried out for 7 days, using eight land-based Each equation represents the rate of change of each biological
mesocosms (2.25 m depth) that each contained 1500 L of St. Lawrence
compartment, expressed as an algebraic sum of inputs and outputs.
Estuary surface water previously passed through a 240 lm Nitex screen.
Table 1 gives the definition and units of the different parameters
Pairs of mesocosms were submitted to four UVB treatments: natural UVBR
and a set of possible values obtained after fitting the model to data
as control, low UVBR enhancement, high UVBR enhancement and no
UVBR. The UVB intensities were increased using lamps. In the fourth from the natural UVBR treatment. We fitted the model to data from
treatment natural UVB radiation was removed by a 0.13 mm Mylar D sheet.
(22), obtaining good results (Fig. 2). A first look shows that the
Dynamics of ciliates (length, 15–35 lm), heterotrophic flagellates (2–10
model can be considered a reasonable representation of the
lm), heterotrophic bacteria (,1 lm), small phytoplankton (,5 lm) and
real system. The fitting was performed by maximum likelihood
large phytoplankton (5–20 lm) were monitored during the experiment. To
fit our model we used data corresponding to the first treatment (natural regression analysis, using parameters without constraints and mini-
UVBR) and then we simulated an enhancement of UVBR by means of an mizing the quadratic differences between predicted and observed
increase its possible effects, as explained below.
values for each biological variable. Figure 2 shows the fit for small
Model construction and sensitivity analysis. To build a mathematical
phytoplankton (Fig. 2a), large phytoplankton (Fig. 2b), heterotro-
model, we must have a clear picture of the biological problem to be studied.
phic flagellates (Fig. 2c) and bacteria (Fig. 2d). The model approx-
In this case, mesocosm experiments were carried out using a simplified
community, constituted only by phytoplankton, bacteria (B) and small imates data very well for all variables with the exception of
zooplankton; mesozooplankton, similar to microcrustaceans, were excluded
bacteria. In this case the model exhibits a more fluctuating dynamic
by prefiltration. After experimental observations, the model considered
than the real data (Fig. 2d).
two phytoplankton fractions: small phytoplankton (Fc; cells 1–5 lm long)
A closer look at the model shows that the large phytoplankton
and large phytoplankton (Fg; cells 5–20 lm long). Zooplankton was
also subdivided in two fractions: ciliates (C) and heterotrophic flagellates (Fg) is autonomous (i.e. it does not depend on other compartments)
(Fh). and its equilibrium point is given by Fg* 5 (A2 À m2 À ex2)/B2.
We considered a conceptual model with two additional compartments
This compartment is a donor but it has no controllers. The system
connecting biological boxes: detritic particulate organic carbon (POC) and
can be reduced again, this time to four equations:
dissolved organic carbon (DOC). However, these two boxes were not
included in the mathematical formulation, as explained below. Figure 1
represents the conceptual model; each box is a variable, thin arrows
represent fluxes and wide arrows represent possible deleterious effects dFc
¼ FcðA1 À B1 Fc À m1 À ex1 À p1 CÞ
of UVBR.
dt
This system involves seven compartments and is expressed by a very
dB
complex set of equations that may become untreatable from a mathematical ¼ Bðe1 ex1 Fc À m3 À p3 CÞ
dt
point of view. Fortunately, we can simplify the problem and reduce its
dC
dimensionality by eliminating the two organic carbon boxes and shifting
¼ Cðe3 p2 Fh þ e4 p3 B þ e5 p1 Fc À m4 Þ
them to an implicit form. The mortality of bacteria is directly linked to dt
feeding by heterotrophic flagellates; similarly, the excretion rate of small
dFh
phytoplankton is linked directly to bacteria nutrition. Moreover, we can ¼ Fhðe2 m3 B À p2 C À m5 Þ
dt
simplify the dynamic system as follows: only the phytoplankton fractions
Photochemistry and Photobiology, 2006, 82 905
Table 1. Mean of each parameter in the model, units and values obtained
fitting the model to experimental data (19) without UVR addition.
Symbol Definition Units Fitted value*
DayÀ1
A1 Intrinsic rate of increase of 1.6
small phytoplankton
L dayÀ1 cellsÀ1
B1 Self-limiting term of small 5 E-5
phytoplankton in the
logistic equation
dayÀ1
m1 Mortality rate of small 0.02
phytoplankton
dayÀ1
ex1 Excretion rate of small 0.001
phytoplankton
(producing DOC)
dayÀ1 cellsÀ1
p1 Rate of predation of small 6 E-4
phytoplankton by ciliates
À1
A2 Intrinsic rate of increase of day 0.3
large phytoplankton
L dayÀ1 cellsÀ1
B2 Self-limiting term of large 5.08 E-7
phytoplankton in the
logistic equation
dayÀ1
m2 Mortality rate of large 3 E-4
phytoplankton
dayÀ1
ex2 Excretion rate of large 0.02
phytoplankton
(producing DOC)
e1 Efficiency of DOC Nondimensional 0.006
assimilation by bacteria
dayÀ1
m3 Mortality rate of bacteria 0.003
dayÀ1 cellsÀ1
p3 Rate of predation of bacteria 0.009
by ciliates
e3 Efficiency of heterotrophic Nondimensional 4.3 E-4
flagellates conversion by
ciliates
dayÀ1 cellsÀ1
p2 Rate of predation of 5 E-5
heterotrophic flagellates
by ciliates
e4 Efficiency of bacteria Nondimensional 9 E-5
conversion by ciliates
e5 Efficiency of small Nondimensional 0.001
phytoplankton assimilation
by ciliates
dayÀ1
m4 Mortality rate of ciliates 0.6
dayÀ1
m5 Mortality rate of 0.005
heterotrophic flagellates
cellsÀ1
e2 Efficiency of heterotrophic 3 E-5
flagellates assimilation
eating dead bacteria
*E-4 5 310À4, E-5 5 310À5, and so on.
Finding the four population equilibria, we verify that there is
only one condition of coexistence for the four populations. This
condition is given by:
p3 ðA1 À m1 À ex1 Þ À m3 p1
*
Fc ¼
Figure 2. Model fitted to experimental data of natural UVBR treatments;
ex1 e1 p1 þ p3 B1
small phytoplankton (Fc) (a), large phytoplankton (Fg) (b), heterotrophic
ex1 e1 p2 ðA1 À m1 À ex1 Þ þ B1 ðp3 m5 À p2 m3 Þ þ m5 ex1 e1 p1 flagellates (Fh) (c) and bacteria (B) (d).
B* ¼
e2 m3 ðex1 e1 p1 þ p3 B1 Þ
ex1 e1 ðA1 À m1 À ex1 Þ À B1 m3
Under natural UVBR conditions there is an indirect effect
C* ¼
ex1 e1 p1 þ p3 B1 between the three types of prey eaten by ciliates: bacteria, small
Fh* ¼ f½e4 e1 ex1 p2 p3 ðA1 À m1 À ex1 Þ phytoplankton and heterotrophic flagellates. This effect can be
þ e5 p1 e2 m3 ðp3 A1 þ p1 m3 À p3 m1 À p3 ex1 Þ understood in two ways. The first interpretation is to consider a
top-down effect by which the ciliates regulate their three prey. If
À e4 p3 ðm3 p2 B1 À m5 ex1 e1 p1 À p3 m5 B1 Þ
true, any increase in the population of one type of prey should be
À m4 e2 m3 ðex1 e1 p1 þ p3 B1 Þ=
a consequence of the predator’s preference for another type of prey.
½e3 p2 e2 m3 ðex1 e1 p1 þ p3 B1 Þg The second possibility is a regulation that combines bottom-up and
906 Fernando Momo et al.
Sensitivity analysis
In order to clarify the results, we performed a sensitivity analysis in
which one parameter at a time was varied in a fixed proportion and
we measured the output variation in each variable. The results are
shown in Fig. 4.
Considering only the higher sensitivities (a 10% variation in the
parameter produces a minimum variation of 5% in the output),
we can see that Fc is a self-controlled variable: the significant
sensitivities are for its own growth parameters (A1 and B1) (Fig.
4a). In the case of ciliates the control factors are related to the
growth efficiency of the most abundant prey (bacteria) (i.e. ex1 and
e1) and with the dynamics of one secondary prey (small phyto-
plankton) (i.e. A1 and B1) (Fig. 4b). As a consequence there is
a bottom-up control of ciliates.
As we can see in Fig. 4c heterotrophic flagellates are controlled
both by predators (ciliates) and by prey (bacteria), because the
variable Fh is sensitive to p3 and e4 (the parameters that regulate
the predation of ciliates over bacteria) and to e2 (the transformation
efficiency when eating bacteria). As a consequence heterotrophic
flagellates have one bottom-up and three top-down controls.
Finally, bacteria are totally controlled by the predator ciliate
because bacteria are mainly sensitive to p3, e4 and m4 (Fig. 4d); the
first two are predation parameters and the third is the predator
mortality rate.
Analysis of the equilibrium expression reveals that a small
phytoplankton population will increase if the predation on bacteria
is higher (p3 increases), the mortality of bacteria increases (m3) or
the term B1 decreases (less self-competition). The first effect (an
Figure 3. Effect of increase mortality rates (increment of 10%) in increase of small phytoplankton population when p3 increases) is
all compartments simulating UVBR effects in bacteria (a) and hetero- given for a sort of ‘‘preference’’ of the predator for bacteria; this
trophic flagellates (b). NUV 5 natural UVBR dose, UV 5 UVBR
preference is given by a higher efficiency of capture ( p3). The
enhanced 10%.
second effect (an increase in small phytoplankton population when
m3 increases) may represent an indirect effect: if bacteria mortality
top-down effects. In this case, growth in one prey causes a predator is higher, heterotrophic flagellates have more food and their
population increase (bottom-up effect) and the enhancement of population grows; ciliates are offered more flagellates and eat less
predation pressure on the other prey types produces a diminution in on Fc. The third effect (small phytoplankton equilibrium increases
this prey population (top-down effect). In the latter case the growth when B1 decreases) is a simple self-competition effect. All these
of one of the prey compartments produces the decrease of the other effects are deducible from the equilibrium point expression.
two by improving the predator (C) population. This kind of effect Ciliates benefit from a slight increment in the mortality rate of
is called ‘‘apparent competition’’ (23,24): there is no competition bacteria (m3) because Fc and Fh increase and there is more prey
for resources but the population dynamics mimic the competition biomass for ciliates. Therefore, ciliates eat more phytoplankton and
dynamics because each increase the population of one type of prey heterotrophic flagellates and bacteria can grow again. Another
produces a decrease in the other two prey populations. The interesting result is the counterintuitive effect of p3 (the predation
mathematical expressions for equilibrium suggest that this last efficiency over bacteria): when ciliates have high efficiency, their
interpretation may be the correct one. equilibrium biomass is lower, which indicates that, for ciliates, it is
an advantage to be a ‘‘prudent’’ predator sensu (25).
The effect of UVBR
We simulated the UVR effects as an increment of 10% in all
DISCUSSION
mortality rates. This approach is not perfect because different
organisms have different sensitivities to UVR and show different The importance of bacteria and bacterivory is well established
remediation capacities. On the other hand, it is necessary to (19,26). Heterotrophic bacteria use dissolved organic matter to
emphasize that these mortality rates are really the expression of build up their cellular material and the newly formed bacterial
a net effect between damage and repair in each biological com- biomass is transferred to metazoans via protozoan bacterivory
partment. Despite these limitations we consider that our approx- (mainly heterotrophic ciliates). Our results show that, under simple
imation is roughly correct because we can model changes that assumptions, the dynamics of a planktonic system with phyto-
closely match field observations: bacteria benefit from UVBR plankton, bacteria and protozoa can be simulated and studied.
because of a decrease in the ciliate predation (Fig. 3a) and the same Protozoan bacterivory may be considered a key process in
effect is evident for heterotrophic flagellates (Fig. 3b). Small and recovering a considerable part of the primary production that
large phytoplankton were not affected by the UVBR increase in would otherwise be lost to aquatic food webs and is believed
the model. to indirectly impact carbon flux dynamics by regulating standing
Photochemistry and Photobiology, 2006, 82 907
stocks, species composition and metabolic activity of the bacterial
community. In our model it is evident that ciliates regulate bacteria,
heterotrophic flagellates and small phytoplankton populations
and that this dynamic can cause surprising results via indirect
interactions, such as the apparent competition between bacteria and
small phytoplankton that have a common predator (24).
A major problem of contemporary science is to understand the
structure and dynamics of complex systems. In particular, the
model presented here is focused on the response of the whole
community to UVBR stress and it emphasizes the importance of
biological interactions in determining that response. Our model is
capable of simulating the community response to UVBR. When
a UVR increase is simulated by adding the same percentage of
mortality to all biological compartments, bacteria, heterotrophic
flagellates and small phytoplankton benefit from the relaxation of
predation pressure. This result coincides with field and experi-
mental observations (22). It is clear that UVR can affect the
bacterivory by protozoa; for instance, a loss of motility and,
consequently, a decrease of the bacterivory of the heterotrophic
nanoflagellates after their exposure to UVB has been reported
(17,22). However, we demonstrate that a prey increase is not
necessary the result of a differential damage between prey and
predators; in fact, the coexistence equilibrium is moved toward
a situation with more prey and less predators simply by introducing
the same increase in mortality rates for both populations Although
this result is similar to the found in the most classic work in
predation (27), it is probably the most important topic to take into
account in the interpretation of experimental data and in the
prediction of future scenarios.
UVRB effects on communities may not be explained only by
differences in damage/repair ratios among species. Changes at the
community level are complex and characteristic of high levels of
organization. As demonstrated by the sensitivity analysis, small
changes in some parameters may produce dramatic alterations in
community composition at equilibrium. In particular, if UVBR
decreases predation coefficients ( p1, p2, p3), all of the populations
change and the whole community is driven to a new equilibrium
point.
Another modeling study found indirect effects in planktonic
communities (18). That model was similar to the one presented
here but the nutrients dynamics were explicitly included, showing
apparent mutualism among phytoplankton and bacteria. In our
model nutrients are not explicitly included and the main indirect
effect is an ‘‘apparent’’ competition between bacteria and small
phytoplankton due to predation.
The good fit with the data suggests that our formulation (without
nutrients) can be sufficient to analyze the global behavior of this
kind of community. We can assume that, in conditions of nutrient
depletion, the stronger indirect effect will be mutualism (18);
however, an increment in nutrients supply to nonlimiting con-
ditions will probably show apparent competition as the most
important effect. This effect is due to increased predator popu-
lations. This kind of variable interaction has been reported in the
ecological literature (28). Evidently, more studies are necessary in
Figure 4. Sensitivity analysis for the parameters in the short model. Bars
order to extend these kinds of models to field conditions. Although
show the percentage variation in the output produced by a 10% variation in
mesocosms can be considered better experimental models than
each parameter (in abscissa). Negative values indicate that an increment in
microcosms (Belzile et al., this issue), they do not include all the the parameter produces a decrease in the variable. Sensitivities of Fc (a),
physical effects that we find in the field, such as vertical mixing, sensitivities of C (b), sensitivities of Fh (c) and sensitivities of B (d).
the larger phytoplankton, the cascade effects produced by large
zooplankton (e.g. crustaceans or appendicularians) and the
dynamics of nutrients, DOC and POC. In particular, in field
908 Fernando Momo et al.
conditions there are DOC and POC inputs and outputs that must 10. Dohler, G. (1997) Effect of UVB radiation on utilization of inorganic
¨
nitrogen by Antarctic microalgae. Photochem Photobiol. 66, 831–836.
be considered to explain the observed patterns. Moreover, organic
11. Fauchot, J., M. Gosselin, M. Levasseur, B. Mostajir, C. Belzile,
matter interacts with UVR and increases its attenuation, and UVR
S. Demers, S. Roy and P. Villegas (2000) Influence of UV-B radiation
produces the photobleaching of DOC and POC (29,30). However, on nitrogen utilization by a natural assemblage of phytoplankton.
in the mesocosm experiments used to test the fit the model there J. Phycol. 36, 484–496.
12. Goes, J., N. Handa, S. Taguchi and T. Hama (1994) Effect of UV-B
were no extra sources of DOC or POC.
radiation on the fatty acid composition of the marine phytoplankter
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CONCLUSIONS Ser. 114, 259–274.
13. Buma, A., E. Van Hannen, M. Veldhuis and W. Gieskes (1996) UVB
The model presented here shows a combination of very important radiation induces DNA-damage and DNA-synthesis delay in the
new results, which is very rewarding because of the simplicity of marine diatom Cyclotella sp. Sci. Mar. 60, 101–106.
14. Mostajir, B., T. Sime-Ngando, S. Demers, C. Belzile, S. Roy,
the model. It presents a very good fit with experimental obser-
M. Gosselin, J. Chanut, S. de Mora, J. Fauchot, F. Vidussi and
vations both under normal and UVBR-enhanced conditions. It
M. Levasseur (1999) Ecological implications of changes in cell size
gives reasonable predictions about the UVBR effects in planktonic and photosynthetic capacity of marine Prymnesiophyceae induced
communities, showing nontrivial dynamics and identifying critical by ultraviolet-B radiation. Mar. Ecol. Prog. Ser. 187, 89–100.
15. Davidson, A., H. Marchant and W. de la Mare (1996) Natural UVB
parameters that control these dynamics. It allows us to study the
exposure changes the species composition of Antarctic phytoplankton
whole community dynamics, given details about each population
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Acknowledgements—This work has been supported by an award from the
18. Aota, Y. and H. Nakajima (2000) Mathematical analysis on co-
Inter American Institute for Global Change Research (grant CRN-026).
existence conditions of phytoplankton and bacteria systems with
We thank Dr. Jose E. Ure for his assistance with solving some mathemat-
´
nutrient recycling. Ecol. Model. 135, 17–31.
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19. Chatila, K., S. Demers, B. Mostajir, M. Gosselin, J.-P. Chanut and
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