Supplementary materials
Parameter estimates used to vital rate of tilapia population
Intrinsic survival probability
Pathiratne (1999) showed that the percentage survival of O. mossambicus fry under
non-exposure condition. Therefore, the parameters (b and k) of intrinsic survival
probabilities (S0(t)) can be estimated by using the Eq. T1-8 to fit the survival data.
Species-specific growth coefficient (A0)
Chen et al. (2012) showed that the body mass of 14 days old larva and 30 days old
juvenile under non-exposure condition were 0.008 ± 0.002 (mean ± SD) and 0.025 ±
0.15 g wet wt. Huang (2010) showed that the body mass of 210, 217, 224, 231, and
238 days old adult under non-exposure condition were 8.74 ± 2.44, 9.85 ± 3.23, 11.41
± 4.28, 13.09 ± 5.3, and 13.44 ± 5.58 g wet wt. This study used the West growth
model (Eq. T3-1) to fit the body mass data from Chen et al. (2012) and Huang (2010)
for estimating the species-specific growth coefficient (A0) under non-exposure
condition.
Body burden for x% maximum growth inhibition
This study used the Hill-based stander 3-parameter sigmoidal dose-response equation
to fit the published data of larva and adult growth inhibitions (Wu et al., 2003; Huang,
2010) to estimate the body burden for 50% maximum growth inhibition (IEC50) and
calculate the IEC10 and IEC1 of larva and adult stages,
E (t , Cb ) 
E max
 IEC 50( t ) 

1  
Cb


n
,
(S1)
where E is the growth inhibition (–), Emax is the maximum growth inhibition (–), Cb is
the body burden (μg g-1), and n is the Hill coefficient (–). Then, using the IEC10 and
IEC1 in adult stage to estimate the growth rate parameters in juvenile stage by Eqs.
(T3-3) – (T3-5).
Fecundity parameters
This study conducted the relationship between body mass and fecundity, and to
estimate the fitted coefficients (m and d) by using the Eq. (T1-7) to fit the body
mass-dependent fecundity data from Riedel (1965).
Survival rate (σ)
The estimates of b and k can be substituted into Eq. T1-8 for predicting the intrinsic
survival probabilities (S0(t)) (background survival probabilities without pollutants)
and the TK/TD parameters (k1, k2, kr, and kk) can be substituted into threshold damage
model for predicting the survival probabilities (S(t))of life-stage tilapia exposed to
pulsed Cu activities. Then, linking the estimates of S0(t) and S(t) at same time t to
estimate the survival rate (σ) by using Eq. T1-4.
Growth rate (γ)
Wb0, Wmax0 and A0 can be substituted into the West growth model for describing the
growth trajectories of tilapia under non-exposure condition. Then stressed effects on
growth for tilapia were occurred when tilapia exposed to pulsed Cu activities.
Therefore, the IEC10 and IEC1 of larva, juvenile, and adult stages can be substituted
into stress function (Eq. T3-3) and applied to reflect the different mode of action on
growth effects. Then, the stress function and the West growth model could be linked
to predict the growth trajectories of tilapia under pulsed Cu activities exposures.
Fertility rate of adult stage (F3)
This study assumed that only in adult stage had fertility capacity. First, we used the
estimates of m and d to estimate the mass-dependent fecundity (Fei(W(t)). Here, we
link the time-dependent mass with the mass-dependent fecundity for conducting the
relationship between age and fecundity. Then, the daily fecundity rate can be estimate
by the differential of age-specific fecundity. Second, the daily fecundity rate
multiplied by E and Fm can be estimated the fertility rate (F3).
Population abundance
Fig. S1 shows stage-specific population abundance over a 2-generation projection for
constant and Cu-pulse exposure populations using initial individual of 10 as input. In
the constant exposure populations, stage-specific tilapia abundance followed a
monotonic increase fashion over time (Fig. S1a – c). Compared to the constant
exposures, the pulsed scenarios A and B produced relatively the largest reduction in
abundance in all stages over time (Fig. S1d – i). In view of projection matrix [A], the
probabilities of surviving and staying in larval stage (P1) decreased from 0.6049 –
0.0002 and 0.7841 – 0.0057, whereas the probabilities of surviving and growing from
larval to juvenile stages (G1) decreased from 0.0121 – 4.65×10-6 and 0.0157 – 0.0001,
respectively, with increasing pulsed Cu activities, for pulsed scenarios A and B, and
thus provided the explanation. A notable finding was that pulsed scenario C produced
a similar projection over time of stage-specific population abundance with that of the
constant exposures (Fig. S1a – c, j – l).
Larvae
Juveniles
Adults
Constant exposure
15
15
a
Cu activity
Control
12
12
12
9
9
6
6
3
3
3
0
0
0
1.6
1.8
2.0
9
6
5
400
200
0
200
0
d
400
0
4
4
3
3
2
2
2
1
1
1
0
0
400 0
0
3
200
5
200
400
0
Median pulsed frequency scenario
5
5
g
h
4
4
4
3
3
3
2
2
2
1
1
1
0
0
400 0
0
200
15
400
k
12
12
9
9
9
6
6
6
3
3
3
0
0
0
200
400
200
400
200
400
200
400
i
0
12
0
400
0
200
Low pulsed frequency scenario
15
15
j
200
f
e
Cu activity
1.5–3
1.5–6
1.5–9
0
c
High pulsed frequency scenario
5
5
4
Log (population abundance)
15
b
0
200
400
l
0
Age (d)
Fig. S1 Population abundances of tilapia in a, d, g, j larval, b, e, h, k juvenile, and c, f,
i, l adult stages exposed to different waterborne constant and sequential pulsed
exposure scenarios varied with Cu activities (g L-1).
Reference
Chen WY, Lin CJ, Ju YR, Tsai JW, Liao CM (2012) Assessing the effects of pulsed
waterborne copper toxicity on life-stage tilapia populations. Sci Total Environ
417-418: 129-137
Huang YH (2010) Biokinetic and biodynamic modeling approach to characterize
chronic copper toxicity and ecophysiological response of tilapia (Oreochromis
mossambicus). Master’s Thesis, China Medical University, Taiwan, ROC
Pathiratne A (1999) Toxicity of fenthion in Lebaycid to tilapia, Oreocheomis
Mossambicus (Peters): Effects on survival, growth and brain acetylcholinesterase
activity. J Natl Sci Found Sri Lanka 27:79-91
Riedel D (1965) Some remarks on the fecundity of tilapia (T. mossambica Peters) and
its introduction into middle Central America (Nicaragua) together with a first
contribution towards the Limnology of Nicaragua. Hydrobiologia 25:357-388
Wu SM, Jong KJ, Kuo SY (2003) Effects of copper sulfate on ion balance and growth
in tilapia larvae (Oreochromis mossambicus). Arch Environ Con Tox 45:357-363