Article
pubs.acs.org/est
Population-Level Modeling to Account for Multigenerational Effects
of Uranium in Daphnia magna
Pierre-Albin Biron,† Sandrine Massarin,‡ Frédéric Alonzo,‡,* Laurent Garcia-Sanchez,‡ Sandrine Charles,†
and Elise Billoir†,§
Université de Lyon, F-69000, Lyon; Université Lyon 1; CNRS, UMR5558, Laboratoire de Biométrie et Biologie Évolutive, F-69622,
Villeurbanne, France
‡
Institut de Radioprotection et de Sûreté Nucléaire (IRSN), DEI, SECRE, LME, Cadarache, France
§
Plateforme de Recherche ROVALTAIN en Toxicologie Environnementale et Ecotoxicologie, 1 avenue de la gare - BP
15173 - Alixan, F-26958, Valence Cedex 9, France
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See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
†
ABSTRACT: As part of the ecological risk assessment associated with
radionuclides in freshwater ecosystems, toxicity of waterborne uranium
was recently investigated in the microcrustacean Daphnia magna over a
three-generation exposure (F0, F1, and F2). Toxic effects on daphnid life
history and physiology, increasing over generations, were demonstrated at
the organism level under controlled laboratory conditions. These effects
were modeled using an approach based on the dynamic energy budget
(DEB). For each of the three successive generations, DEBtox (dynamic
energy budget applied to toxicity data) models were fitted to experimental
data. Lethal and sublethal DEBtox outcomes and their uncertainty were
projected to the population level using population matrix techniques. To
do so, we compared two modeling approaches in which experimental
results from F0, F1, and F2 generations were either considered separately
(F0-, F1-, and F2-based simulations) or together in the actual succession
of F0, F1, and F2 generations (multi-F-based simulation). The first approach showed that considering results from F0 only
(equivalent to a standard toxicity test) would lead to a severe underestimation of uranium toxicity at the population level. Results
from the second approach showed that combining effects in successive generations cannot generally be simplified to the worst
case among F0-, F1-, and F2-based population dynamics.
■
generations.9 In contrast, results with copper suggested that
daphnids may develop a resistance with an increasing survival
rate when parents were previously exposed.10 These contrasting
results highlight the necessity for multigenerational tests, as toxic
effects observed over one generation may under- or overestimate the real effects of pollutants on a longer term. In the
case of depleted uranium (U), a previous study demonstrated an
increase in sensitivity across three generations of D. magna.11
A dynamic energy budget approach applied to toxicology
(DEBtox) was used to address possible mechanisms of action of
depleted U.12 DEBtox models mechanistically describe how
metabolic costs induced by toxicant exposure come at the
expense of energy-dependent processes, including somatic
growth and reproduction.13,14 The previous study shows that
a decrease in carbon assimilation efficiency is likely and
sufficient to explain observed effects in D. magna exposed to
depleted U. This mechanism has been confirmed by
complementary assimilation measurements using radiolabeled
INTRODUCTION
Today it is recognized that ecological risk assessment can
markedly improve its biological relevance by considering
responses to contaminant exposure at the population level rather
than at the organism level.1 From this prospective, population
models are particularly helpful tools that allow multiple toxic
effects observed under laboratory experiments on organism
survival and fecundity to be combined into one population-level
endpoint, such as the asymptotic population growth rate. Priority
has been recently given to the use of matrix population models2
for their prospective potential in modeling population health,
including the effects of toxic compounds on the different age or
development stages of organisms within populations.3−6
Studying toxic effects under multigenerational exposure
regimes represents another key issue to improve the ecological
relevance of risk assessment because natural populations can be
exposed to toxicants over several generations. Until now, such
multigenerational studies are scarce and their outcomes vary
widely among tested pollutants. In Daphnia magna, exposure to
waterborne nickel showed increasing effects on growth across
two generations7 and on offspring size across seven generations.8 Similarly, increasing sensitivity of daphnid reproduction
and survival to americium-241 was observed across three
© 2011 American Chemical Society
Received:
Revised:
Accepted:
Published:
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August 1, 2011
November 21, 2011
November 24, 2011
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in D. magna. Whereas stress functions accounting for sublethal
toxic effects are assumed to depend on internal concentration resulting from bioaccumulation in organisms in the standard
DEBtox,14 Massarin et al. (2011)12 showed that effects of
depleted U on assimilation were immediate and could be linked
to external concentration directly. A rapid kinetics was consistent
with the observation of severe damages to the intestine epithelial cells.
Hence in agreement with Massarin et al. (2011)12 the stress
function for assimilation sA was directly linked to exposure concentration c by
food and microscope observations of histological damages on
the intestinal epithelium.11,12 Having described toxic effects of
depleted U on D. magna life history and physiology, consequences at the population level remain to be examined.
The aim of this study is to explore how increasing effects at
the individual level among the three successive generations
(hereafter referred to as F0, F1, and F2) may alter population
responses to U. To do so, DEBtox and survival models are first
fitted to survival, growth and reproduction data reported in
Massarin et al. (2010).11 Outcomes are then projected from
the organism to the population levels using two modeling
approaches. In the first approach, uranium effect on asymptotic
population growth rate is evaluated in each generation
considered separately, assuming that the population behaves
asymptotically either like F0, F1, or F2. In the second approach,
combined probability of population extinction is investigated,
assuming that the population behaves successively like F0, like
F1 and finally like F2.
sA (c) = max(0, kA(c − NECA ))
(1)
that is, sA is null below a sublethal toxicity threshold NECA and
proportional to the excess above NECA with an effect intensity
coefficient kA.
Growth and reproduction processes were respectively
modeled by the following eqs 2 and 316 given for ad libitum
conditions:
■
dl
2
(t , c) = rB
(1 − sA (c) − l(t , c))
dl
2 − sA (c)
L
with l(0, c) = l0 = 0
Lm
MATERIAL AND METHODS
Experimental Data. Body length, fecundity, and survival
data were taken from previously performed experiments with
daphnids exposed to waterborne depleted U.11 Briefly,
D. magna was continuously exposed at four treatments
corresponding to depleted U concentrations of 0, 10, 25, and
75 μg L−1 for three generations F0, F1, and F2. F0 was initiated
with freshly released neonates (<24 h) from the fifth brood
obtained from cultures. F1 and F2 were launched with
individuals aged <24 h from the fifth brood from previous
generations, exposed under the same conditions as their parents.
Survival and reproduction were monitored daily for 21−24 days
using three replicate bottles containing 20 daphnids each. Body
length was measured in neonates and in adults at depositions
of brood 1, brood 3, and brood 5 using five replicate daphnids
per treatment. All experiments were performed under optimal
laboratory conditions for the tested species, meeting the
reproductive requirements of OECD guidelines15 in the control.
Organism-Level Modeling. Toxic effects of depleted U
on somatic growth and reproduction were modeled at the
organism level using equations of the DEBtox model14 modified
by Billoir et al. (2008a).16 Massarin et al. (2011)12 recently
showed that among the five possible modes of action proposed
by the DEBtox approach (increase in maintenance costs, an
increase in growth costs, a decrease in assimilation, an increase
in egg production costs, or a mortality during oogenesis)
depleted U likely acted through a decrease in carbon assimilation
R (t , c ) =
(2)
Rm ⎛
⎜(1 − sA (c))(l(t , c))2
3⎜
1 − lp ⎝
⎞
⎛ 1 + l(t , c) ⎞
⎜
⎟ − l p3⎟⎟ if l(t , c) ≥ l p
⎝ 1 + (1 − sA (c)) ⎠
⎠
R(t , c) = 0 otherwise
with R(0, c) = 0
(3)
where at time t and exposure concentration c, l(t,c) is the scaled
body length (divided by the maximum body length, Lm) and
R(t,c) is the reproduction rate (number of eggs per mother per
day). All parameters are defined in Table 1.
For controls, the daily survival probability was assumed
independent of age. For exposed organisms, potential effects
were modeled by a stress function ss to survival, analog to sA:
ss(c) = max(0, ks(c − NECs))
(4)
where NECS is the lethal toxicity threshold and kS is the effect
intensity coefficient for survival.
Table 1. Parameters Involved in the Organism-Level Models (DEBtox and Survival) and Their Prior Distributionsa
symbol
dimension
interpretation
prior distribution
L0
Lm
rB
lp
Rm
NECA
kA
m
NECS
kS
mm
mm
d−1
(−)
egg. d−1
μg L−1
μg−1 L
(−)
μg L−1
μg−1 L
initial volumetric length
maximum volumetric length
Von Bertalanffy growth rate
scaled length at puberty
maximum reproduction rate
no effect concentration for the stress on assimilation
intensity coefficient for the stress on assimilation
blank daily probability of death
no effect concentration for the stress on survival
intensity coefficient for the stress on survival
Norm(1, 0.12) T(0,)
Norm(4.77, 0.592) T(L0,)
Norm(0.11, 0.032) T(0,)
Norm(0.49, 0.072) T(L0/Lm,)
Norm(10.74, 3.622) T(0,)
logUnif(−4,4.31)
logUnif(−10, log((1−lp)/(75-NECA)))
logUnif(−10,−4.5)
logUnif(−4,4.31)
logUnif(−15,0)
source
expert
Billoir
Billoir
Billoir
Billoir
expert
none
Billoir
expert
none
knowledge
et al. (2008b)17
et al. (2008b)17
et al. (2008b)17
et al. (2008b)17
knowledge
et al. (2011)18
knowledge
a
(−) means dimensionless. Norm(me, sd2) denotes a normal distribution with a mean me and a variance sd2. T(a,b) denotes interval censoring
between bounds a and b (see Plummer (2010)19 for details). logUnif(inf, sup) denotes a loguniform distribution, meaning that the natural logarithm
of the random variable is uniformally distributed between inf and sup.
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The probability S(t,c) to be alive at time t and exposure
concentration c was given by
S(t , c) = ((1 − m)(1 − ss(c)))t
(5)
where m is the blank daily probability of death.
Parameters of effect models at the organism level (Table 1)
were estimated for each experimental generation F0, F1, and F2
separately. Estimation was carried out by Bayesian inference, a
technique which combines prior probability distributions of
parameters and data likelihood to return parameter estimates
as posterior distributions. Prior distributions were chosen
according to available information,17,18 and were identical for all
generations (Table 1).
Data likelihood was assumed binomial for survival (number
of survivors conditional on the number at the previous time
point) and normal for growth (body length in mm). Likelihood
for reproduction data, expressed as the time-cumulative number
of eggs per mother Rcum (t,c) = ∫ 0t R (t,c) dt, was assumed
negative binomial parametrized so that its mean equaled the
model output. Growth and reproduction models (eqs 1−3)
were fitted simultaneously because they were interdependent
and shared common parameters (NECA and kA). Survival
model (eqs 4 and 5) was fitted separately. In the first generation (F0), no organism died in the range of concentrations
tested. Hence, the stress function for survival ss was set to 0
independent of the concentration.
Bayesian inference was performed using Markov Chains
Monte Carlo (MCMC) algorithms implemented in the rjags R
package.19 For each estimation process, three independent
MCMC chains were run in parallel. For each chain, after an
initial burn-in period of 150 000 iterations, the Bayesian algorithm
was run for 25 000 000 iterations and parameter posterior distributions were sampled every 500 iterations. Replicated data
were simulated and recorded for posterior predictive checking.20
Population-Level Modeling. Outcomes of organism-level
modeling (survival and DEBtox) were projected to the
population level using age-classified population models with a
time step of one day. Life-cycle graphs were represented with
21 age-classes per generation (Figure 1, A and B). Survival and
fecundity rates were specific of both age and generation.
In each generation F (F0, F1, or F2), daphnids were assumed
to pass from age i to i+1 according to age- and generationspecific survival rates Pi,F(c) calculated considering the survival
function SF(t, c) (eq 5) calibrated for F and assuming a birth
pulse model and a prebreeding census:21
S (t(i + 1), c)
Pi,F(c) = F
SF(t(i), c)
Figure 1. life-cycle graphs considered in the two approaches for
population-level modeling: (A) F0-, F1-, and F2-based populations
and (B) multi-F-based population. a1 denotes the first adult age-class.
Two different approaches were considered in order to project
toxic effects from the organism to the population. First,
population dynamics were based on experimental results from
generations F0, F1, and F2 considered separately (Figure 1, A).
This approach aimed to investigate whether experimental results
from F0, F1, and F2 might yield significantly different impacts
on λ. Results were respectively referred to as F0-, F1-, and F2based populations. The asymptotic population growth rate (λ)
was calculated as the dominant eigenvalue of the Leslie matrix
(21 × 21) where fecundity rates were reported in the first row,
and survival rates in the subdiagonal. Note that λ (also known as
finite rate of population increase) relates to another common
population index, the intrinsic rate of population increase r,
with r = ln(λ). In the framework of matrix population models,
any asymptotic population growth rate (λ) below 1 predicted
theoretical population extinction. Second, experimental results
from the different generations were considered jointly using a
population model which accounted for the three successively
exposed generations (Figure 1, B). This approach aimed to
explore cases where the population might go extinct in generation F0 and F1. Results were referred to as multi-F-based
population. To do so, daphnids in F0 (respectively F1)
produced offspring in F1 (respectively F2) while daphnids in
subsequent generations were assumed to be similar to those in
(6)
A term G21,F(c) = 0.95× P20,F(c) was added to loop into the
last age-class of each generation, as calibrated for D. magna.22
Age- and generation-specific fecundity rates Feci,F(c) were
calculated from DEBtox reproduction functions RF(t, c) (eq 3)
calibrated for each generation F (F0, F1, or F2). Daphnid
offspring are released as free-swimming neonates three days
after egg deposition in the brood pouch. For this reason, a delay
of three days was introduced in eq 7 to account for maturation
from eggs to neonates. We assumed a birth pulse model and a
prebreeding census:21
Feci ,F(c) =
∫i
i+1
P1,F(c)RF(t − 3, c)dt
(7)
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Table 2. Posterior Distributions (I.E. Estimates) of the Parameters of the Organism-Level Models (DEBtox and Survival)a
F0
F1
F2
symbol
dimension
mode (95% CI)
mode (95% CI)
mode (95% CI)
L0
Lm
rB
lp
Rm
NECA
kA
m
NECS
kS
mm
mm
d−1
(-)
egg. d−1
μg L−1
μg−1 L
(−)
μg L−1
μg−1 L
0.97 (0.93−1.1)
4.3 (4.2−4.4)
0.14 (0.13−0.16)
0.57 (0.55−0.60)
11 (10−12)
0.10 (0.021−4.0)
1.8 × 10−3 (1.5−2.0) × 10−3
0.11 × 10−3 (0.051−0.79) × 10−3
ne
ne
1.0 (0.93−1.1)
4.4 (4.3−4.7)
0.10 (0.089−0.11)
0.58 (0.54−0.61)
12 (11−14]
7.1 (1.1−7.8)
6.1 × 10−3 (5.5−6.6) × 10−3
0.23 × 10−3 (0.056−1.7) × 10−3
23 (18−24)
2.2 × 10−3 (1.7−2.9) × 10−3
1.0 (0.90−1.1)
4.4 (4.1−4.5)
0.12 (0.10−0.13)
0.57 (0.52−0.60)
14 (12−16)
0.044 (0.02−0.87)
5.7 × 10−3 (5.2−6.4) × 10−3
0.08 × 10−3 (0.081−3.52) × 10−3
2.4 (0.16−53)
0.4 × 10−3 (0.0−12) × 10−3
a
(−) means dimensionless and ne is for not estimated. Empirical statistics of posterior distributions are given as the mode and the 95% credibility
intervals (calculated as (2.5−97.5% percentiles) of posterior distributions).
sensitive to U than F1- and F2-based populations, in accordance
with observations at the organism level. Overlapping confidence intervals indicated that sensitivities of F1- and F2based populations did not significantly differ. Uncertainty was
larger for F2-based population-level projection compared to
F1-based.
In generation F0, organism-level effects of depleted U were
limited to sublethal endpoints (no mortality) and F0-based
population-level impacts remained weak: at the highest tested
concentration (75 μg L−1) the asymptotic population growth
rate was (94−96)% of its control value. F1- and F2-based
population-level effects of depleted U were much stronger than
in the F0-based population, resulting from both sublethal and
lethal effects at the organism level. For example, at 50 μg L−1
the asymptotic population growth rate λ was (83−87)% of its
control value for F1 and (70−90)% for F2.
Multi-F-Based Population. The extinction probability of
the multi-F-based population remained null below 26 μg L−1
then increased from 0 to 1 between 26 and 72 μg L−1 (Figure 3, B).
At exposure concentrations from 26 to 68 μg L−1, the
population extinction was exclusively due to criterion C3 (F2based λ below 1), meaning that the population would become
extinct in the long term. Between 68 and 72 μg L−1, extinction
was caused either by criterion C2 (no reproduction in F1) or by
criterion C3. Above 72 μg L−1, extinction was exclusively due
to criterion C2 (no reproduction in F1). Extinction due to
criterion C1 (no reproduction in F0) did not occur within the
tested concentration range.
F2. According to the life-cycle graph (Figure 1, B), three
successive extinction criteria were considered:
• criterion C1: extinction in F0 if Feci,F0(c) = 0 whatever
the age i,
• criterion C2: extinction in F1 if the population survived
F0 and Feci,F1(c) = 0 whatever the age i,
• criterion C3: extinction in subsequent generations if the
population survived F0 and F1 and F2-based asymptotic
population growth rate becomes lower than 1.
Monte Carlo simulations were performed in order to take
account of model uncertainty at the organism level. For each
generation, 1000 parameter sets were drawn from their joint
posterior distribution (Table 2). For each parameter set,
survival and fecundity rates were then calculated (eqs 6 and 7)
over the range of uranium concentrations (from 0 to 75 μg L−1
with a concentration increment of 1 μg L−1) and the
corresponding λ and extinction probability were derived.
■
RESULTS
Organism-Level Modeling. Parameter estimates obtained
from the three distinct generations F0, F1, and F2 (Table 2)
were compared according to their 95% credibility intervals
(calculated as (2.5−97.5% percentiles) of posterior distributions). Concerning nontoxicological parameters, parameter
estimates obtained for the three generations were not significantly different among generations (Table 2), except the body
growth rate rB which was significantly higher for F0 than F1.
Toxicity threshold estimates (NECA, NECS) were not significantly different among generations. In contrast, intensity coefficients of sublethal stress functions (kA) were significantly
higher in generations F1 and F2 than in generation F0,
indicating an increase in sensitivity to uranium when maternal
pre-exposure occurred.
For the three considered life history traits (growth, reproduction, and survival), posterior predictive checking was performed
(Figure 2). Second generation organisms (F1) exposed to
75 μg L−1 did not reproduce. Hence, no third generation data
(F2) could be collected for this exposure concentration. Almost
all observed data were within the corresponding 95% credibility
interval of replicated data (Figure 2), denoting a good quality
of fit.
F0-, F1-, and F2-Based Populations. Relative asymptotic
population growth rate (compared to the control) varied significantly among generations on the range of depleted U concentration (Figure 3, A). The F0-based population was less
■
DISCUSSION
Uranium concentrations range from 0.02 to 6 μg L−1 in natural
freshwaters and may reach 2 mg L−1 in the vicinity of uraniferous sites, reflecting the composition of surrounding rocks.23
Higher concentrations, exceeding background values, have been
reported in some ecosystems due to human activities such as
mining, extraction, refining, and processing of uranium for
nuclear fuel or weapons.24 Ecotoxicological values calculated
from laboratory toxicity tests on a wide range of species showed
a great variability among studies.25 In cladocerans, both acute
and chronic toxicity differed among tested species mainly as a
result of differences in alkalinity, hardness and pH,26−30 which
strongly influences uranium speciation and bioavailability.31
In D. magna, water concentrations causing 50%-lethality at 48 h
ranged from 0.39 to 51.9 mg L−1 and 50%-effect on 21-day
reproduction was reported from 91 to 520 μg L−1.32−34 Data
used in this paper were collected under the water conditions
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Figure 2. posterior predictive checking for growth, reproduction and survival (first, second and third row, respectively) of D. magna exposed to
depleted U over three successive generations (first, second, and third column, respectively). Observed data (points) and corresponding 95% credible
intervals of replicated data distributions (segments) were superimposed for a visual assessment of goodness-of-fit. Time points were slightly shifted
horizontally among treatments for clarity. Treatments were represented in different shades of gray.
that both increased uranium bioavailability and respected physiological limits of D. magna, as suggested by Zeman et al.
(2008).34 Their calculated concentration of 14 μg L−1 yielding
10% chronic effect on reproduction after 21 days was therefore
consistent with our estimated NEC for growth and reproduction, the 95% CI of which ranged from 0.020 to 7.75 μg L−1
independent of the generation. Effects on survival rose from
no observed mortality up to a concentration of 75 μg L−1 in
generation F0, to 15% mortality after 23 days at 25 μg L−1 and
100% mortality after 16 days at 75 μg L−1 in generation F1.
Even though NEC for survival was not determined in F0,
the estimated 95% CI ranged from 0.157 to 52.5 μg L−1,
independent of the generation. This is consistent with the
uranium concentration yielding 50% acute lethality after 48 h of
390 μg L−1 reported by Zeman et al. (2008).34
In a recent study Massarin et al. (2011)12 assessed the mode of
action of depleted U by fitting DEBtox models to the same data
set. This previous study considered reproduction expressed as
the produced mass of eggs whereas the present study considered
the number of offspring for the sake of demographic projection.
Nevertheless, our results were in agreement with earlier findings
that changes in uranium toxicity across generations are related to
an increase in intensity coefficient, rather than to a reduction in
NEC.12 In fact, on the basis of 95% credibility intervals changes
in NEC for growth and reproduction was not significantly
different among generations, whereas the estimated intensity
coefficient was significantly greater for F1 and F2 than for F0.
From a statistical point of view, the larger uncertainty of
inference results and population-level projection obtained for
F2 as compared to F0 and F1 (Figure 3, A) can be explained by
the smaller number of data. In fact, because of mortality and
lack of reproduction in F1, the toxicity test for F2 was performed with one less exposure concentration (75 μg L−1) than
for F0 and F1, and a reduced initial number of organisms (10
instead of 20) at 25 μg L−1. In the Bayesian framework, parameters are considered as random variables having probability
distributions that reflect uncertainty. This provides explicit
and complete information for any comparison of interest (for
instance between-generation comparisons in our case) and
enables the translation of uncertainty into projection and/or
extrapolation simulations, as done to assess population-level
impacts.
At the population level, the first approach adopted may seem
inconsistent in the context of multigeneration studies. Indeed,
matrix models are meant to describe the dynamics of successive
generations, whereas they were used as projection tools for the
effects experimentally observed in one generation at a time and
for the three experimental generations independently (F0-, F1-,
and F2-based populations, Figure 1, A), as done in Raimondo
et al. (2009).5 Such an approach can only address the following
scenarios. What if risk assessment relied on population-level
projection of ecotoxicity tests performed with organisms: whose
parents were not exposed (F0-like)? whose parents were exposed
(F1-like)? whose parents and grand-parents were exposed
(F2-like)? Actually, F0-like daphnids produced F1-like offspring
and F1-like daphnids produced F2-like offspring. The multi-Fbased population model we proposed (Figure 1, B) attempted to
mimic this process and our results showed that in the case of
uranium effects observed on generations F1 and F2 combined.
The extinction probability was the result of what happened in
both F1 and F2. In other words, the population extinction
occurred sometimes before a third-generation was reached,
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speculative in absence of additional experimental results. In fact,
uranium effects may further increase in severity in subsequent
generations or reflect the development of a resistance in
D. magna. Understanding the underlying mechanisms which
cause the observed increase in uranium effects across generations
would allow extrapolating from one exposed generation to the
next. However, experiments designed by Massarin et al. (2010)11
aimed to show potential changes in effects over generations, not
to explain underlying mechanisms. Increasing sensitivity to
uranium across generations may be due to (1) a reduced energy
investment per offspring, as suggested by the observed reduction
in mass of eggs in exposed females, (2) genetic alterations
occurring in germinal cells and transmitted to the progeny35
and/or (3) direct exposure of embryos in the brood chamber36
in generations F1 and F2 (but not in generation F0 which was
exposed from the neonate stage). Additional experiments are
necessary to address these different hypotheses and clarify the
underlying mechanisms or to examine effects of uranium in a
longer term (to stabilization across generations?).
One underlying assumption of our modeling approach is that
sensitivity to uranium is comparable among daphnids from
different instars and equal to that experimentally observed for
the fifth brood.11 However, susceptibility might vary depending
on instar number, as demonstrated with another metal. In fact,
daphnids from early instars were smaller and were shown to
be more sensitive to cadmium toxicity than daphnids from
late instars.37 Thus one can hypothesize that susceptibility to
uranium might differ among instars, inducing stronger effects in
early F1 cohorts than in late ones. Conversely, if sensitization is
a gradual process, one can expect that an early F1 cohort might
be less susceptible than a late F1 cohort. Such scenarios may
have different consequences for population dynamics, affecting
to some extent conclusions from our modeling approach.
The population level is acknowledged to be ecologically
more relevant than the organism. In this context, ecological risk
assessment would markedly improve with the consideration of
realistic environmental conditions,38 especially food regimes in
the context of this study, in which the toxicant affects food
acquisition and assimilation. Constant ad libitum food, as in our
study, is not representative of the natural situation in which
population responses to uranium may differ under episodically
limited food levels. Including realistic food regimes in the
model requires first experimental studies of uranium effects at
different food levels. The severity of uranium effects could be
reduced with decreasing food, as was observed with cadmium39
or lindane.40
To conclude, the coupling of DEBtox and survival models
with matrix population models proves to be a relevant tool.
However, our study suggests that matrix population models can
be misleading if multigenerational aspects are omitted. In the
case of uranium, considering solely first-generation daphnids
leads to a severe underestimation of the population response.
Furthermore, our results showed that the effects observed in
successive generations combined such that population dynamics
cannot generally be simplified by examining only the most
affected among several generations.
Figure 3. population-level endpoints derived in the two approaches for
population-level modeling: (A) asymptotic growth rate of F0-, F1-, and
F2-based populations and (B) probability of extinction of the multi-Fbased population along with the stacked area chart of the three criteria
(C1−C3).
sometimes from the third-generation onward. This demonstrates
that the effects experimentally observed in successive generations
have to be accounted for in a combined way and gives credence
to the multi-F-based approach.
Our multi-F-based population model described the dynamics
of a theoretical population in which the two first generations
behaved like F0 and F1, and every following generation like F2.
This simple assumption was made as a first attempt to project
results of multigenerational toxicity tests to higher levels of biological organization. Simulating changes in effect severity from
F3 onward would be very relevant, but would remain highly
■
AUTHOR INFORMATION
Corresponding Author
*Phone: +33 4 42 19 95 79; e-mail: frederic.alonzo@irsn.fr.
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ACKNOWLEDGMENTS
We are grateful to Dr. Tom Hinton for commenting on and
editing this manuscript. We would like to thank four anonymous
referees for their relevant comments that significantly improved
this manuscript.
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