Environ. Sci. Technol. 2009, 43, 7895–7901
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Extinction Risk of Exploited Wild
Roach (Rutilus rutilus) Populations
Due to Chemical Feminization
W E I A N , †,‡ J I A N Y I N G H U , * ,†
J O H N P . G I E S Y , §,|,⊥ A N D M I N Y A N G ‡
Laboratory for Earth Surface Processes, College of Urban and
Environmental Sciences, Peking University,
Beijing, 100871, China, Research Center for
Eco-Environmental Sciences, Chinese Academy of Sciences,
Post Office Box 2871, Beijing 100085, People’s Republic of
China, Department of Veterinary Biomedical Sciences and
Toxicology Center, University of Saskatchewan, 44 Campus
Drive, Saskatoon, SK, S7N 5B3, Canada, Department of
Zoology and Center for Integrative Toxicology, Michigan State
University, East Lansing, MI, and Department of Biology and
Chemistry, Research Centre for Coastal Pollution and
Conservation, City University of Hong Kong, 83 Tat Chee
Avenue, Kowloon, Hong Kong
Received March 22, 2009. Revised manuscript received
August 20, 2009. Accepted August 24, 2009.
A model that assesses risks posed by feminization to wild
populations of roach was developed. A population life table
matrix model that considered both sexes and a newly developed
fertility kinetic function was applied to calculate the intrinsic
population growth rate (λ) of roach populations where males had
been feminized. The maximum sustainable yield (MSY) was
used to quantify the effect of various degrees of feminization
on sustainability of exploited fisheries. Risk of extinction was
calculated for wild roach populations. The results of the
simulations suggested that (a) In the absence of fishing pressure
λ would only be decreased 1.5-1.7% even in the presence
of a 100% incidence of intersex; (b) in the presence of selective fishing, the occurrence of intersex could significantly
increase the extinction risk of local roach populations; (c) the
benchmark value for the severity index of intersex and sex
ratio required for a sustainable population of roach were estimated
to be 1.13 and 0.57, respectively. The approach presented
here provides a tool to (1) understand effects of male’s feminization
on population dynamics; (2) assess extinction risk of wild
roach populations from feminization; (3) assist environmental
managers in making policy decisions relative to fishery resource
conservation.
Introduction
Recently, feminization of male fish due to exposure of
endocrine disrupting chemicals (EDCs) has been observed
in freshwater and marine environments throughout the world
(1-6). In particular, feminization of male roach was prevalent
in lakes and rivers of the United Kingdom, where the
* Corresponding author phone/fax: 86-010-62765520; e-mail:
hujy@urban.pku.edu.cn.
†
Peking University.
‡
Chinese Academy of Sciences.
§
University of Saskatchewan.
|
Michigan State University.
⊥
City University of Hong Kong.
10.1021/es900857u CCC: $40.75
Published on Web 09/11/2009
 2009 American Chemical Society
proportion of male roach exhibiting intersex was reported
to be as great as 100% (7). Changes in the structure of the
testes results in lesser fertility of feminized male fish (8, 9).
In a whole lake experiment conducted in Canada it was found
that 17β-ethynylestradiol at 5-6 ng /L caused feminization
of males and a subsequent collapse of wild populations of
fathead minnow (Pimephales promelas) (10). However, the
17β-ethynylestradiol concentration was relatively low (0-0.37
ng/L), where the high incidents of intersex in roach but
relatively low severity of intersex have been observed in
natural fish populations (3). Until now, it has been unclear
how to quantify the effects of feminization of male fish on
the overall fitness of wild fish populations in natural
environments, especially in exploited populations. Thus, it
has been difficult to assess the potential effects of chronic
exposures to these compounds and their risk on ecologically
relevant end points.
Because the roach is a species in which feminization of
males is often observed in European rivers and adequate
information was available on population structure and
dynamics, a two-sex, age-classed, population model was
developed to assess potential effects of feminization on roach.
Specifically, the objectives of this study were to determine
(i) the magnitude of effects on population dynamics and
demography to clarify whether the intersex could affect
persistence of a wild roach population; (ii) the critical
parameters (sex ratio, feminization severity (intersex incidence and severity index), etc.) required for the conservation
of fishery resources that should be monitored in wild
populations. Here we provide a scientific basis for making
policy decisions on fishery resource conservation and
environmental management in the presence of intersex in
males.
Materials and Methods
Procedure of Assessing Potential Effects of Intersex on
Roach Populations. As shown in Figure 1, the procedure for
assessing potential effects of intersex on Roach populations
consisted of two parts: (1) Model establishment and (2) Risk
characterization, of which related notations and interpretations are summarized in Table 1. During model establishment, a fertilization kinetic function was developed and
incorporated into a two-matrix model (11) for simulation of
population dynamics under intersex occurrence. The annual
survivals except for the survival probability of wild roach
from zygotes to first age (P0,1) and fecundity rates at different
ages were estimated from field surveys. P0,1 was calculated
by using Newton’s iteration method (12) to solve a two-sex
matrix, after population growth rate (λ, the dominant
eigenvalue of the matrix) was estimated from the doubling
time (td) of small populations, and the other parameters
(survival and fertility rates) were estimated above. During
risk characterization, we extrapolated individual intersex
occurrence to population response by developing the
relationship between reductions of fertilization rate with
intersex severity which was linked to the two-sex matrix for
λ calculation by the fertilization kinetic function. And then,
λ values under intersex occurrence were used to calculate
the MSY loss and extinction probability of wild roach
populations.
Model Development for Extrapolating from Individual
Intersex to Population Response. The response of wild
populations is often evaluated by using an age-specific twosex population matrix eq 1 (11):
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N0,t+1
0
Nf 1,t+1
Pf1,1
...
...
Nfi,t+1 )
0
Nm1,t+1
Pm1,1
...
...
Nmi,t+1
0
F2
0
...
0
0
...
0
... Fi-1
...
0
...
...
... Pfi,i-1
0
0
...
...
0
0
0
0
0
0
..
...
0
0
0
0
...
...
0 Pmi,i-1
|| |
N0,t
0
Nf1,t
0
...
...
0 × Nf i,t
Nm1,t
0
...
...
Nmi,t
(1)
where N0,t is the total number of zygotes at time t; Nfi,t and
Nmi,t represent the number of males and females at time t
and age class i, respectively; Pfi,j and Pmi,j are the survival
rates per year of individual females and males, respectively;
and Fi is fertility rate, which is calculated by the fertilization
kinetic function.
Sexual reproduction that depends on separated males
and females, and can be affected by alterations in reproductive fitness of males and females as well as environmental
factors. In fact, sexual dimorphism to maturity and differences
in reproductive performance among ages are common in
many species. Thus the function describing fertility rate
should be age-specific and include both sexes (11). Because
roach reproduce by external fertilization of eggs with sperm
in the water, one male can fertilize the eggs of several females
or one female can spawn with several males at the same time
(13). Therefore, at any given time, there can be some
redundant males or females in the spawning population.
Considering these conditions, a fertilization function (eq 2)
was developed to describe the fertilization process of fish,
of which derivation details are given in SI Section I.
F ) φf
kδ(1 - pq)
0.241 × (1 - δ) + δ(1 - pq)
(2)
where φf is probability of a female mating relative to the total
number of female adults; k is fecundity rate (i.e., average
number of eggs per female every year); δ is the sex ratio,
which is defined as the proportion of males in the spawning
subpopulation; p is the incidence of intersex in the population
of spawning males; and q is the reduction of fertilization rate
caused by intersex.
European roach spawn from April to June in shallow water,
and eggs hatch within 4-10 days. The number of eggs
spawned (i.e., clutch size) is directly proportional to the length
and weight of the female. Although a local natural population
can be divided into three subpopulations: reserve, recruitment, and residue, and only residue subpopulation was
reported to attend the spawning troop (14). So, it is necessary
to consider the mating probability (φ) of individuals in the
total population when predicting population dynamics.
However, there is no information on mating probability of
roach available in the literature. In this study, mating
probability was described as the proportion (%) of mating
individuals in the total population, and was estimated using
the population proportion of spawning in the whole roach
population of different ages which has been extensively
surveyed in Jelesna Brook, Russia (14). Considering that
proportions of male (φminmi) and female (φfinfi) roach in the
spawning population of different ages (i) can affect the
probability of eggs being fertilized, sex ratios (δ) were
calculated by eq 3.
18
δ)
∑φ
minmi
i)2
18
∑
i)2
(3)
18
φminmi +
∑
φfinfi
i)2
where nm and nf are the stable population age structure
vectors at different ages (i) calculated by the two-sex matrix.
The magnitude of k can be predicted based on the body
length by use of a regression on data collected during a field
survey conducted between 1975 and 2000 (15). The optimized
equation between k and female body length (TL, cm) (eq 4)
was selected from different empirical relations, and the details
for optimizing and selecting were shown in SI Sections II
and III.
log10(k) ) 3.08 × log10(TL) + 0.5637 n ) 77,
r2 ) 0.8331 p-value < 0.05 mse ) 0.0505
(4)
where n is sample size. The log10 transformation bias was
estimated to be the exponent of the normal distribution with
a mean of 0 and standard deviation of 0.225 (root square of
mse) was used to estimate the predictive error in the
uncertainty analysis.
FIGURE 1. Framework for assessing the ecological risk of wild roach population caused by intersex incidents. P0,1: survival
probability of wild roach from zygotes to first age; λ: populations growth rate; rm: intrinsic rate of population growth, which is equal
to the natural logarithm of λ.
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Life Cycle Parameters. Fertility Rate (Fi). Roach reproduce
by spawning in which gametes are released into the water
and fertilization takes place outside of the bodies of the
male and female fish. Roach often assemble at spawning
sites prior to spawning (13), and therefore males and
females can still find each other even if the density of the
total population is small. Since most populations of roach
in Europe are exploited, there is little chance that they
would become locally overpopulated. For these two reasons
no density-dependent limit was used in the simulation
model. Thus, in natural environments in the absence of
intersex occurrence fertility rates can be calculated by eq
2 where p and q are 0 and δ ) 0.5.
Annual Survival Rates (Pi,j). The roach (family Cyprinidae)
is a small freshwater and brackish water fish with a native
range that extends across Europe (15, 16). The life cycle of
roach can be divided into four stages: (1) Zygotes, which is
the combination of gametes produced by adult male and
female; (2) Larvae, which have no significant sex differentiation characteristics; (3) Adult males and females; (4) Gametes
produced by adult males and females (Figure 2). When
gametes produced by male and female fish fuse to form
zygotes through the fertilization process, the life cycle is
repeated. Longevity of roach has been reported to be as long
as 18 years. The annual mean mortality rate of the roach
populations in the Orava Valley Reservoir is about 0.5, which
is nearly identical to that for the populations in the Dyje
River and Klicava Reservoir in Czechoslovakia (14). The
survival rate per year (Pi,j) except for survival of zygotes to
1 year (P0,1) was replaced by the average annual survival rate
in a given period of life, which can be estimated based on
its catch curve (eqs 5, 6) (14, 17).
Ln(Nt) ) a-Zt
Si-j ) e
FIGURE 2. Schematic diagram representation of roach (Rutilus
rutilus) life cycle. Pi: the possibility of survival in age i;
Subscript i: the sequence of age (i.e., 1, 2,.. .0.18 year); Up to
now, the longest longevity of male was observed to be 9 and
female to be 18; So the sequence of adult male is from 2 to 9
years and that of female from 3 to 18 years (14). Subscript f (or
m): the sex female (or male) gs: the average clutch size of male
gametes every year at age i; ge: the average clutch size of
female gametes every year at stage i; Fi: the fertility rate.
Survival of Zygotes to 1 Year. Because it is difficult to
monitor the numbers of zygotes and fry in the field, P0,1 have
been unknown, which has limited the capability to develop
population models. Since the λ of roach populations can be
estimated from doubling time (td) for roach using eq 7 (15),
and other life-cycle parameters have been estimated, the
survival from zygotes to 1 year was determined by use of
Newton’s iteration method (11, 18).
Ln(λ) ) Ln(2)/td
(5)
-Z
(6)
where Si-j is average annual survival from i to j age; Z and
a are the slope rate and intercept of fitted catch curve. Nt is
the fish abundance in a given age-t group (t, year).
(7)
Assessing Roach Population Risk from Intersex Occurrence. Roach Egg Fertilization Reduction due to Intersex. An
experiment evaluating the effects of intersex in male roach
on fertilization was conducted with fish taken from the Rivers
TABLE 1. Notations and Interpretations for Assessing Extinction Risk of Exploited Roach Populations due to Chemical
Feminization
symbol
description
symbol
description
Nt
fish abundance in a given
age-t group (t, year)
Fi
Z
slope rate of fitted catch curve
p
a
intercept of fitted catch curve
q
R
fertilization rate coefficient
δ
φ
average annual survival from i
to j age
sex ratio
mating probability
γ
MSY
n
scalar in vector Nt
Bm
k
average egg clutch size
ai,j
TL
female body length
w
λ
population growth rate
v
td
time required for a quantity to
double in roach population
size
BMSII
Nt
population vector of individual
roach in different ages
BMSR
M
∆MSY/MSY
population transition matrix
proportion of MSY Loss
MSC
mse
rm
intrinsic rate of population
growth
Pi,j
intersex severity index
maximum sustainable yield
maximum original size of
unexploited population
traits of matrix M
stable age structure
distribution
reproductive value distribution
severity index of intersex
corresponding to 10%
predetermined increase of
∆MSY/MSY.
sex ratio corresponding to 10%
predetermined increase of Ψ
from background
model selection criteria
mean squared error
annual survival rates of
individual females and males
from i to j age
Si-j
fertility function
incidence of intersex in
spawning males
lost fertilization potential
caused by intersex
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Aire and Calder in Yorkshire, the River Arun in Sussex, the
River Blackwater in Surrey, and the River Lea in Hertfordshire
of the U.K. The results of these studies were used to develop
a relationship between the rate of fertilization and degree of
pathological changes (i.e., intersex) in testes. The q value for
the fish with only ovarian cavities in testes was about 21.7%,
while that by males containing some testicular ovarian
follicles was approximately 28%, and males that were
classified as being severely feminized exhibited a 77%
reduction (9). To quantify the adverse effects on fecundity
due to intersex, a severity index of intersex (γ) was defined
as a variable to describe the degree of intersex pathological
changes in testes. The values of the severity index of intersex
that corresponded to the three pathologies were 1.0, 2.5, or
5.5, respectively. The boundary conditions were set such that
q was equal to 18.5% when γ ) 0 (normal males), and q was
100% when γ ) 7 (complete feminization of males) (9). The
optimized severity index of intersex (γ)-response (q) curve
(eq 8) was selected from different empirical relations (details
are in SI Section IV.
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q ) exp(0.2534γ - 1.743)n ) 5, mse ) 0.0027,
p-value < 0.05
(8)
where mse is mean squared error.
Extraploating from Individual Intersex to Population. The
dominant eigenvalue of the two-sex population matrix was
regarded as population growth rate per year (λ) over a unit
time period, and the corresponding right eigenvector represented the stable age structure (11) which was calculated
by use of Matlab Ver. 6.5. MSY is the largest catch that can
be taken from a species’ stock over an indefinite period, and
reflects a balance between fish harvesting rate (19) and its
λ, and it can be calculated using eq 9.
MSY ) ln(λ)Bm /4
(9)
where Bm is the maximum original size of the unexploited
population. The quotient of MSY loss (i.e., ∆MSY) due to
intersex occurrence under exposure to EDCs and the MSY
in the natural environment (i.e., ∆MSY/MSY), was defined
as the proportion of MSY loss, which was calculated by
∆ln(λ)/ln(λ) and applied to relate the effects of intersex
occurrence on the ability of the population to sustain
exploitation.
The value of λ determines whether a population is locally
sustainable. In this study, the population extinction probability (Ψ) with the stress of intersex occurrence, was defined
as the area proportion of λ < 1.0 to the total area under
possible values of severity index of intersex (γ) and incidence
(p) corresponding to effects due to exposure to feminizing
chemicals and individual sensitivities in different habitats.
The Ψ represents the population extinction risk with the
stress of intersex occurrence. More details about Ψ are
illustrated in SI Section V.
To obtain a criterion for protection of roach populations
as a fishery resource, the relation between the ∆MSY/MSY
and severity index of intersex at 100% incidence was
established, and then applied to estimate the benchmark
value by the benchmark dose/level methodology (20). The
benchmark value is the dose/level referring to some response
above background (e.g., 10%) and often regarded to be
equivalent with no-observed-effects dose/level, which could
be calculated using Newton’s iteration method (12). In this
study, the benchmark severity index of intersex (BMSII) was
calculated as the severity index of intersex corresponding to
10% predetermined increase of ∆MSY/MSY. And the benchmark sex ratio (BMSR) was the sex ratio corresponding to
10% predetermined increase of Ψ from background.
Sensitivity Analysis. The sensitivity of λ to changing of
life-cycle traits can be calculated using eq 10 which is based
on the two-sex matrix (eq 1).
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∂λ
vw
)
∂aij
⟨v, w⟩
(10)
where aij is the traits of roach life cycle in two-sex matrix (eq
1); w is calculated using the corresponding right eigenvector
with the dominant eigenvalue (λ); v is estimated by the
corresponding left eigenvector with λ. The vw and <v, w >
denotes the cross and scalar product, respectively (11). The
sensitivity was analyzed using Matlab V6.5 software.
Simulation of Multiple Models and Uncertainty Analysis.
Simulation in this study involved multiple models. The
sources of uncertainty were partitioned into two components,
i.e., predictive errors for predicting fertility rate and value
fluctuation of annual survivals. The fertility rates were
predicted by use of the fertilization kinetic function (eq 2)
which was embedded in the relationship between body length
and egg clutch size (eq 4) and the relationship between
reduction of fertilization rate and severity index of intersex
(eq 8), and their predictive errors were estimated by use of
the bootstrapping method. The model describing the relationship between reduction of fertilization rate and severity
index of intersex was optimized using model selection criteria
(MSC) (21) as described in SI Section II (Model Specific Error
and Model Selection) and SI Figure S2. The annual survivals
were simulated by Monte Carlo methods in which distributions (SI Table S1) were derived from a serial data set which
covered different roach natural habitats.
Population responses (∆MSY/MSY, Ψ) were simulated
by use of resampling methods (Matlab version 6.5) (400 trials,
a trade-off between the requirement of uncertainty analysis
and time cost of simulation). The BMSII and BMSR for each
trial were obtained by use of Newton’s iteration method,
respectively, and then the cumulative probability and density
distribution of the BMSII and BMSR values for all 400 trials
were analyzed by use of the nonparametric method of Statistic
software version 6.5.
Data sets Used for Calibration of Multiple Models. The
original data in the multiple models consist of fish abundance
in different habitats, average eggs per female, doubling time
and reduction of fertilization rate with intersex pathological
changes. The abundances of fish at different ages as shown
in SI Figures S4-S13 were collected from different habitats
in Europe (13-15, 23), and were used to estimate the
probability distribution of annual survival rates. The td of
roach (1.4-4.4 years) was reported only for the UK (16), and
its probability distribution was assumed to be uniform. The
average egg numbers per female with body length from field
investigation (11) and reduction of fertilization rate with
intersex pathological changes based on field experiment (9)
were applied to predict the fertility rate of roach under intersex
occurrence.
Results and Discussion
Estimation of Roach Life Cycle Parameters. The annual
survivals of roach depend on environmental factors such as
food abundance, predators, climates, conditions, and so on.
Therefore, survival rates among specific habitats are always
different. The age composition has been reported for catches
of roach from 1930 to 1941 in watersheds of the Norfolk
Broads, Rivers Cam, and Shepreth Brook at Barrington, the
Old West River, and River Granta in Cambridgeshire, the
Grantham Canal, and other locations in Europe (13, 22). Based
on these age compositions of catches, catch curves were
fitted using eqs 5-6 and shown in SI Figures S4-S13, from
which the annual male survival rates of age III-XVIII class
groups were 0.4975 (SD: 0.1414) and that of female were
0.5291 (SD: 0.1459), and annual survivals of males and females
of age classes I-III were estimated to be 0.118 (SD: 0.0343)
and 0.123 (SD: 0.0339), respectively (SI Table S1). Using the
catch abundance of spawning roach from Jelesna Brook in
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FIGURE 3. Contour of the roach population growth rate (λ) with intersex occurrence under the best condition (P0,1 ) 0.022, (a)) and
the worst condition (P0,1 ) 0.079, (b)). The circle represents l of wild roach inhabiting in watersheds in England. Sites A: Labor
control; B-E: lakes and canals without sewage treatment work in England and southern Ireland; Rivers upstream (subscript u): Fu:
Wreake/Eye;Gu:Ouse; Hu: Lea; Iu: Arun; Ju: Nene; Rivers downstream (subscript d): Fd: Wreake/Eye; Gd: Ouse; Hd: Lea; Id: Arun; Jd:
Nene; K: Trent; L: Rea; M: Air.
Russia (14), the ranges of φ of male and female were estimated
to be 0.268-1 and 0.054-1 by SI eq S-24, respectively (SI
Table S2). Thus, the Fi from age classes III-XVII were
calculated to be from 2255 to 73829 based on k and φ by
fertilization kinetic function (eq 2 where p ) 0, q ) 0, and
δ ) 0.5) as shown in SI Table S1. The details of estimating
annual survival rate and mating probability are shown in SI
Section VI. The probability of survival of zygotes to age class
I (P0,1) is unknown for field populations. Using eq 7, the value
of λ for wild roach populations was estimated to be between
1.1712 and 1.6405 based on td (1.4-4.4 years). Thus, using
the λ and other life-cycle parameters, the least and greatest
values of P0,1 were calculated to be 0.022 and 0.079,
respectively by using Newton’s iteration method (12).
Relationship between λ and Intersex Occurrence and
Sensitivity Analysis of Roach Life Cycle Traits. To simulate
the population response affected by intersex in males, values
of “λ” were calculated (eq 1) under intersex occurrences.
Contours of λ were developed across the range of least to
greatest values of P0,1 with values of the severity index ranging
from 0 to 7 and incidences ranging from 0 to 100% were
developed (Figure 3). Values of “λ” were more sensitive to
severity index than incidence of intersex. When the severity
index increased from 0.0 to 6.3 with an incidence of 100%
intersex, the value of “λ” changed from 1.17 to 1.0 at the least
value of P0,1 (Figure 3(b)), whereas λ ranged only from 1.63
to 1.36 within the same changing range at the highest P0,1
(Figure 3(a)). These results suggest that the species with the
lesser value of P0,1 would be more susceptible. The susceptibility of species to pollutants depends on their life- cycle
variables, as exemplified by the population persistence
analyses for threatened and endangered species in lab (23).
Mean values of roach life-cycle parameters (SI Table S1)
were used to determine the sensitivity to λ (eq 1). The results
of this sensitivity analysis provided profiles of uncertainty
sources in the two-sex matrix population model. Fertility
rate (Fi) and survival (P0,1) from zygotes to age class I
contributed for more than 90% of the variation in population
growth rate (SI Figure S14).
Effects of Intersex on Wild Roach Populations and
Uncertainty Analysis. In recent years, several typical EDCs
such as 17β-estradiol, 4-nonylphenol, dioxin, and bisphenol
A (24-27) have been detected in rivers of England which
receive effluents from sewage treatment works. At the same
time, relatively great incidences of intersex has been observed
in wild populations of roach in eight rivers, the Air, Arun,
Lea, Nene, Ouse, Rea, Trent, Wreake/Eye, and some lakes
and canals throughout the British Isles (3, 7, 9). The incidence
(4-18%) and severity index of intersex (0.19-0.50) in the
lakes and canals were both less than those in the upstream
(11.7-44% for incidence and 0.60-0.95 for severity index)
and downstream (16-100% for incidence and 0.68-2.32 for
severity index) of the eight rivers. Such intersex conditions
resulted in 19.8-21.7%, 20.2-27.5%, and 20.2-31.1% reduction of fertilization rates in lakes and canals, upstream and
downstream reaches of the eight rivers according to eq 8
TABLE 2. Prediction of the Intrinsic Population Growth Rate (λ) and Loss of Maximum Sustainable Yield (MSY) of Roach Caused
by Intersex in the UK with Average Value of Life Cycle Parameters
rivers/lakes
Wreake/Eye
Ouse0.177
Lea
Arun
Nene
Wreake/Eye
Ouse0.22
Lea
Arun
Nene
Trent
Rea
air
locations
river upstream
0.62
river downstream
0.68
lake
incidence
severity index
fertilization reduction
predicted λ
MSY loss (%)
0.25
0.199
0.12
0.32
0.44
0.16
0.202
0.57
0.82
1
0.32
0.38
1
0.60
1.404
0.86
0.95
0.81
0.69
1.403
1.40
1.39
1.85
0.49
0.68
2.32
0.198
0.21
0.212
0.217
0.209
0.202
0.42
0.244
0.244
0.275
0.192
0.202
0.311
1.403
0.42
1.404
1.402
1.400
1.404
0.21
0.63
1.05
0.21
1.397
1.393
1.387
1.402
1.401
1.383
1.68
2.52
3.79
0.63
0.84
4.64
VOL. 43, NO. 20, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
7899
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Publication Date (Web): September 11, 2009 | doi: 10.1021/es900857u
FIGURE 4. Cumulative probability and probability density
distribution of the benchmark severity index of intersex (BMSII)
which is defined as the severity index of intersex of
no-observed-effects on maximum sustainable yield (MSY). The
BMSII is the lower 90% confidence interval bounds of severity
index of intersex, corresponding to a 10% predetermined
increase of ∆MSY/MSY. The cumulative probability curve (red
line) was fitted using Matlab version 6.5 software as Percent
(%) ) 224 × normcdf (BMSII, 3.1, 1.36).
(Table 2), respectively. The corresponding λ of wild roach
populations in these watersheds were calculated to be 1.177
to 1.159 (1.52% different) and 1.651 to 1.623 (1.69% different)
at the least and greatest values of P0,1, respectively (Figure
3). This result suggests that even if a 100% incidence of
intersex occurred, it was unlikely to cause the collapse
of local roach population due to the low severity index of
intersex.
MSY is a common index to assess the effects of many
environmental conditions on fishery resource. In this study,
the proportion of MSY predicted to be lost (∆MSY/MSY) was
used as an index to assess the ecological effects of intersex
occurrence in English watersheds (Table 2). The proportion
of MSY loss of roach population with intersex in English
watersheds was estimated to be 7.8-9.2% and 3-3.6% at the
least and greatest values of P0,1, respectively (eq 9).
To calculate a criterion for protection of roach populations
as a fishery resource, the ∆MSY/MSY response was simulated
by use of resampling methods (400 trials). In each trial, one
BMSII would be obtained. From all trials, the cumulative
probability and density distribution of BMSII was developed
by the nonparametric method using Statistic software version
6.0 (Figure 4). The result indicates that when the mean value
of severity index of intersex is less than 1.13, there would be
less than 10% probability that intersex occurrence would
significantly affect MSY. Alternatively, if the value is more
than 4.5, the probability of affecting the MSY would be more
than 90%. In the Nene River and Air Lake of England, the
probabilities to affect MSY were approximately 20 and 28%,
respectively. The BMSII was estimated to be 1.13 and 4.5 at
the lower and upper 90% confidence interval bounds,
corresponding to a 10% predetermined increase of ∆MSY/
MSY (Figure 4). This provides the direct reference value
against which to assess the effects of the of intersex
occurrence in roach population.
Ecological Significance of Intersex under Selective
Fishing and Uncertainty Analysis. Roach, is harvested as a
valuable fish across Europe. In most locations, roach
populations are managed to achieve MSY by allowing only
males to be taken (28, 29). Until the mid-1960s, the ratio
between male and female roach estimated from seine catches
in Europe, was approximately 1:1. Due to the selective fishing
for males from the populations of roach in the Volga delta
7900
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 43, NO. 20, 2009
FIGURE 5. Cumulative probability and probability density
distribution of the benchmark sex ratio (BMSR) which is regarded
as the severity index of intersex of no-observed-effects on
increase of extinction risk (Ψ). The BMSR is the lower 90%
confidence interval bounds of sex ratio, corresponding to a 10%
predetermined Ψ. The cumulative probability curve (red line) was
fitted using Matlab version 6.5 software as percent (%) ) 635 ×
normcdf (BMSR, 2.34, 0.119).
and in the Ural region, populations consisted of more than
90% female in the period from 1995 to 1999. Similar sex biases
have been observed in commercial catches of roach in
Azerbaijan (61-65% females) and Turkmen (57-98% females) (15).
To analyze the effects of intersex occurrence under
selective fishing on the potential of roach populations to
become locally extinct, an index of extinction probability
(Ψ) was calculated. To estimate the effects of intersex
occurrence in the presence of male-selective fishing, the Ψ
value of the wild roach populations was calculated with sex
ratios (δ) ranging from 0.5 to 1. The probability of extinction
(Ψ) as a function of sex ratio (δ) was simulated by the use
of the same methods as above (400 trials) (see SI Section
VII). In each trial, one BMSR was calculated, which is the sex
ratio corresponding to 10% predetermined increase of Ψ.
The cumulative probability and density distribution of the
benchmark sex ratio (BMSR) were calculated using nonparametric methods (Figure 5). When the sex ratio bias is
less than 0.07, there would be less than 10% probability of
sex ratio bias significantly affecting the local extinction under
the condition of the intersex occurrence. Alternatively, when
the bias is more than 0.39, the probability of affecting local
extinction will be more than 90%. Considering the lower 90%
confidence interval bound, the intersex would exert significant adverse effects on the extinction risk of local roach
populations with the sex ratios skewing beyond 0.87. In the
Volga delta and the Ural Rivers, the sex ratio of roach is more
than 0.9, especially in the Turkmen River where the population is 98% female (15). In these two places, the probabilities
of causing local extinction of the roach populations were 91
and 99%, respectively. To further investigate the potential
for local extinctions, the occurrence of intersex in roach
populations should be surveyed in rivers where selective
fishing is applied. From the viewpoint of fishery resource
conservation, the current selective fishing policy should be
modified in the presence of intersex. The result of our study
provides a key reference value for the selective fishing policy
to protect the local resource of fishery.
Overall, we developed an approach to illustrate how to
incorporate histological status of feminization with life-cycle
parameters to extrapolate the response of population and
MSY of wild fish population. Specifically, a modeling
framework is presented to (1) understand the effects of the
intersex occurrence of in male roach on wild populations;
(2) assess extinction risk of wild roach populations under the
stress of feminization; (3) help environment manager to make
policy decisions on fishery resource conservation and
environmental protection due to EDCs exposure.
Acknowledgments
The financial support by the National Natural Science
Foundation of China (40632009) and the National Basic
Research Program of China (2007CB407304, 2006CB403306)
is gratefully acknowledged. The research was supported by
a Discovery Grant from the National Science and Engineering
Research Council of Canada (Project 326415-07) and a grant
from the Western Economic Diversification Canada (Project
6578 and 6807). Prof. Giesy was supported by the Canada
Research Chair program and an at large Chair Professorship
at the Department of Biology and Chemistry and Research
Centre for Coastal Pollution and Conservation, City University
of Hong Kong.
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Publication Date (Web): September 11, 2009 | doi: 10.1021/es900857u
Supporting Information Available
Detailed descriptions of development of fertilization kinetic
function, model specific error and model selection, optimizing relation between egg clutch size and body length,
judgment of intersex diagnose system and optimizing relation
between severity index of intersex and reduction of fertilization rate of roach, illustration of the extinction probability
(Ψ) due to intersex occurrence, estimating annual survivals
of roach and mating probability from field survey, and
uncertainty analysis. This material is available free of charge
via the Internet at http://pubs.acs.org.
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Mississippi River shovelnose sturgeon sampled below Saint
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McAllister, B. G.; Beresford, N.; Henshaw, A. C.; Brighty, G.;
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ES900857U
VOL. 43, NO. 20, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
7901
1
Supporting Information for “Extinction Risk of Exploited Wild Roach (Rutilus rutilus)
2
Populations Due to Chemical Feminization”
3
4
5
6
7
8
9
10
11
12
13
Wei An1,2, Jianying Hu1, John P. Giesy3,4,5, and Min Yang2
1
College of Urban and Environmental Sciences, Peking University, Beijing, 100871, China
Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Post Office Box 2871,
Beijing 100085, People’s Republic of China
3
Dept. Veterinary Biomedical Sciences and Toxicology Center, University of Saskatchewan, 44 Campus
Drive, Saskatoon, SK, S7N 5B3, Canada
4
Department of Zoology, National Food Safety and Toxicology Center and Center for Integrative
Toxicology, Michigan State University, East Lansing, MI, USA
5
Department of Biology and Chemistry, Research Centre for Coastal Pollution and Conservation, City
University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2
14
15
16
17
18
19
20
Pages
Figures
Table
S1-S34
S1-S16
S1, S2
21
22
S1
23
The purpose of this section is to estimate the feasibility of deriving the response of wild
24
roach population caused by chemical feminization using the setup described in our paper. This
25
supporting information provides the detailed calculation and essential explanations of
26
simulating population dynamic of exploited wild roach (Rutilus rutilus) due to chemical
27
feminization.
S2
28
I. Development of Fertilization Kinetic Function. External fertilization is an important
29
issue in fish reproduction, and is easily affected by environmental factors. It is significant that
30
the space of sperm diffusion is infinite in external fertilization, while it is limited in internal
31
fertilization. So the sperm density per egg, activity, quality, and quantity of sperm are
32
important factors in the fertilization of eggs (1) proposed fertilization kinetic function based
33
on egg concentration, sperm concentration, and sperm-egg contact time (2) provided an Eq.
34
S-1 that was simplified by Vogel (1). This simplification can easily be applied in mathematic
35
derivation and can be used to predict the fertilization kinetic of Coral reef fish.
36
During roach spawning, males can fertilize eggs of several females or the eggs of one
37
female can be fertilized by several males. There are several basic types of mating systems,
38
including polygamic, monogamy and others. Spawning of roach is neither polygamic nor
39
monogamic, but rather a type of mix-gamy, called “Lek-Like”, a behavior in which females
40
exhibit preferences for specific males or spawning sites (3). Previously used fecundity
41
functions based on mammals are not appropriate to describe the mating system of roach
42
because of the external versus internal fertilization and the “Lek-Like” spawning instead of
43
polygamy or monogamy. The fertilization kinetic model was developed based on
44
micro-mechanisms in the fertilization process, which can be applied for different mating
45
systems.
The model (Eq. S-1) defined two main factors affecting the fertilization process of eggs,
46
47
i.e., sperm density per egg (S) and fertilization efficacy (u):
48
ω=
49
where ω is the fertilization rate of eggs.
S
u+S
(S-1)
S3
50
In a spawning population, the total eggs (Zf) can be calculated by Eq. S-2.
51
Zf=nf×ge
52
where nf is female number,and ge is egg number per female.
53
Similarly, the total male sperm (Zm) is calculated by Eq. S-3.
54
Zm=nf×gs
55
where nm is male number,and gs is sperm number per male.
56
Based on this definition, the sperm density per egg is calculated by Eq. S-4:
57
s =
58
Z
Z
(S-2)
m
(S-3)
=
f
nm g s
.
n f ge
(S-4)
When inserting Eq. S-4 into Eq. S-1, we can obtain Eq. S-5.
nm g s
n f ge
nm
ω=
=
.
nm g s
ug e
u+
n f + nm
n f ge
gs
59
(S-5)
60
In order to simplify Eq. S-5, a constant coefficient (α) was defined as follows:
61
α=
62
where α is a comprehensive parameter, which is affected by fertilization efficacy, sperm per
63
male and egg number per female per year. So Eq. S-5 can be simplified as Eq. S-7.
64
ω=
65
For male with intersex, p is defined as intersex incidence in spawning population, and q is the
66
reduction of fertilization rate caused by intersex occurrence. Thus, in the spawning population,
67
the available male should be nm(1-pq), which replaces the nm in Eq. S-7. And then the
68
fertilization kinetic function under the intersex condition was derived as Eq. S-8.
69
ω=
ug e
.
gs
(S-6)
nm
αn f + n m
(S-7)
nm (1 − pq)
αn f + nm (1 − pq )
(S-8)
S4
70
In demographic statistics, the sex ratio (δ) is a common parameter of the population age
71
structure, and is defined as the male proportion in the spawning population (Eq. S-9).
72
δ=
73
When Eq. S-9 is introduced into Eq. S-8 to eliminate the nm and nf, fertilization rate (ω) can be
74
calculated by Eq. S-10.
75
ω=
nm
nm + n f
(S-9)
δ (1 − pq )
α (1 − δ ) + δ (1 − pq )
(S-10)
76
The comprehensive fertilization constant (α) represents the quality and quantity of sperm
77
and eggs. Under reference conditions of the absence of intersex (p=0, q=0) and equal numbers
78
of males and females in the population (δ=0.5), the probability of fertilization of eggs was
79
determined to be approximately 0.814 (4). Thus, the fertilization coefficient (α) was estimated
80
to be 0.241 using Eq. S-10.
81
For whole fish population, not all female attend the spawning subpopulation, which is
82
described by the mating probability (φf). When the number of eggs per female every year can
83
be obtained from field by the average clutch size (k), the fertilization kinetic function (F) can
84
be expressed by Eq. S-11.
85
F =ϕf
86
II.Model Specific Error and Model Selection. In usages of regression models based on
87
measured data, ‘‘model specification error’’ can arise when one uses an empirical
88
relationships (linear, exponent etc.) instead of a model that can describe the completed
89
characteristics of a given relation (or process) (6). If the empirical model is more complicated
90
or more parameters are used, we will have an even smaller value of model specific error. To
91
avoid the over-fitting and select the optimal model, model selection criteria (MSC) was
92
applied to compare their relative goodness of fitting among these models (6) considering a
93
trade-off between the model complication and models specification error as expressed by Eq.
kδ (1 − pq )
0.241× (1 − δ ) + δ (1 − pq)
(S-11)
S5
94
S-12
n
∑ we ( x
i
95
MSC = Ln
i
− x)2
i =1
n
∑ wei ( xi − ~xi ) 2
−
2d
n
(S-12)
i =1
96
where xi is the ith observed data; ~
xi is the ith predicted value; x is the mean observed value;
97
n is the number of samples; d is the number of parameters, and wei is the weighting of data. In
98
the range from 2 to 6, the model is acceptable and the higher the MSC, the closer the model
99
explains the observed values (6).
100
III.Optimizing Relation between Egg Clutch Size and Body Length. It is reported that the
101
average eggs clutch size (k) produced by female roach monotonically increased with their
102
body lengths (TLs), of which data were collected in the period from 1975 to 2000 by using
103
field catches in watersheds of Volga river, Ural river, Terek river, Kura river, Atrek river etc. in
104
Europe (7). In general, four kinds of functions were applied to establish the relation between k
105
vs. TL using the linear and nonlinear least square method of Matlab Ver.6.5. as follows:
106
Ln(k)=a×ln(TL)+b
S-13;
107
Log10(k)=a×log10(TL)+b
S-14;
108
Ln(k)=a×log10(TL)+b
S-15;
109
k=10 ( a×ln(TL)+b)
S-16;
110
According to Eq. S-12, MSCs of the Eqs. (S-13-S-16) were calculated using the k and TL data
111
from field survey. The MSC values of Eqs. (S-13-S-15) were 2.0653638, 2.0653643, and
112
2.0653634, much higher than that of Eq. S-14 with MSC of 1.0374046, indicating that Eqs.
113
(S-13-S-15) have almost the same goodness of prediction. In general, the higher the MSC, the
114
better the fitting. Thus, Eq. S-14 was selected for regression between TLs-k due to its slight
S6
115
high MSC.
116
The clutch size and body length transformed by base-10 logarithm were fitted using a
117
regression function “fit” in Matlab Ver. 6.5 using Eq. S-14 (Figure S1), and Eq. S-17 was
118
achieved.
119
Log10(k)=3.08×log10(TL)+ 0.5637
120
The 95% confidence interval of the coefficient “3.08” is 2.763-3.397, and that of “0.5637”
121
was 0.1522-0.9753. mse is the mean squared error. To minify the predictive error in the
122
uncertainty analysis, the data-statistical bias (eε) due to regression-analysis using
123
log-transformed was estimated by Eq. S-18, and the random term was expressed as the
124
exponent of normal distribution with mean of 0 and standard deviation of 0.225 (7) which can
125
be used to calculate the predictive error.
126
eε = emse/2=e0.0252
127
IV.Judgment of Intersex Diagnose System and Optimizing Relation between Severity
128
Index (γ) of Intersex and Reduction of Fertilization Rate of Roach (q). The diagnose
129
system of intersex was established by Jobling et al. where an severity index of intersex fish as
130
a score of 0 indicates a histological male gonad, 1 indicates very slight feminization, >4 but
131
<7 indicates severe feminization, and 7 indicates a histological female gonad (4,9,10). Slight
132
feminization, the ovarian cavity, was regarded as 1; Some oocytes are severer than slight
133
feminization (i.e. 1) and slighter than severe feminization (i.e. 4); The severely feminized
134
tissues are considered between severe feminization and complete female gonad (i.e. 7) (4).
135
Although the judgment was not very accurate, it provided a relative scale for quantifying the
136
effects of fish intersex on fertility rate.
n=77, r2=0.8331, mse=0.0505, p<0.05
(S-17)
(S-18)
S7
137
Although intersex in fish occurs around world, there are only a few data in the field
138
about reduction of fertilization rate due to intersex occurrence. Jobling et.al reported that
139
systemic studies on the roach intersex severity and its effects on fertilization (9). Their studies
140
showed that fertilization rates are reduced 18.5, 21.7, 28, 77.2, 100% under severity index (γ)
141
of intersex of 0, 1, 2.5, 5.5, and 7, respectively, and q increased with γ. In this study, four
142
empirical models were applied to develop the relation between γ and q using the linear and
143
nonlinear least square method of Matlab Ver.6.5. as follows:
144
q=c×γ+d
(S-19)
145
q=exp(c×γ+d)
(S-20)
146
q=Ln(c×γ+d)
(S-21)
147
q=0.185185185 + (1-0.185185185)/(1+10((b-γ)+c))
(S-22)
148
The MSCs of Eqs. (S-19-S-22) using the data set (10) were calculated to be 4.05, 4.83, 2.39
149
and 7.01 using Eq. 12, respectively. Upon using Eq. S-19, the q will be 0.955 when γ=7, while
150
the response variable q is a ratio taking values between 0 and 1, which imply that fertilization
151
rate (4.5%) would exist in population even if all the male became female. However, this is
152
impossible in real world. Eq. S-21 has the similar problem. Eq. S-22 is much better, because
153
when γ=7, the q will be 0.991, very close to 1. However, the MSC of Eq. S-22 is 7.01, much
154
higher than 6. Therefore, Eq. S-22 was excluded for its overfitting with exceptionally good
155
fitting (7). In the case of Eq. S-20, its MSC (4.83) is acceptable. In addition, when γ is over
156
6.9, the q will exceed 1, indicating when γ is more 6.9, and no fertility would exist in
157
population. This is reasonable in natural environment. In fact, it is very difficult to satisfy
158
exactly the condition that q=1 when γ=7 using regression method. Thus, in Eq. S-20, the
S8
159
range of γ was defined to be 0-6.9, and when γ was from 6.9 to 7, the q was set at 1. Taken
160
together, Eq. S-21 was used to fit the relation between severity index of intersex (γ) and
161
reduction of fertilization rate as follows:
162
q=exp(0.2534×γ-1.743)
163
The 95% confidence interval (CI) of the coefficient “0.2534” was 0.1785~0.3282; That of
164
“-1.743” was (-2.21~-1.277). Their stimulated curves of the q-γ were carried out using the
165
bootstrap method (400 trials) shown in Figure S2.
166
V.Illustration of the Extinction Probability (ψ) due to Intersex Occurrence. Population
167
persistence is determined by the population growth rate (λ). When λ is more than 1, the
168
population will remain persistent. When λ=1, the population will be susceptible to extinction.
169
When λ<1, the population will become extinct within several finite generations. In general, a
170
λ of 1 is regarded as a threshold of the population persistence vs. extinction. Thus, when
171
variation of λ was derived by the fluctuation of the environmental factors, the proportion of λ
172
less than 1 was defined as the risk of local population extinction (ψ), which is closely related
173
to the population extinction probability. In Eq.S-11 there are three variables, i.e., intersex
174
incidence, reduction of fertilization rate, and sex ratio, that influence the fecundity of a
175
population. When the sex ratio was a fixed value (such as 0.95, which can occur in a realistic
176
environment), the λ corresponding to the potential changing of severity index (γ) and
177
incidence (p) of intersex can be calculated as shown in Figure S3, where the solid line is the
178
isoline of λm=1 and the deeper color represents the higher λ. The isoline at λm=1 separates the
179
region of a deep red color, of which area was defined as Sλm>1 and a light red color, of which
180
area as Sλm<1. Thus, the proportion of this area (Sλm<1/( Sλm<1+ Sλm<1)) was calculated as the
n=5, p-value<0.05, mse=0.0027
S9
(S-23)
181
risk of local population extinction (ψ), which indicates the probability of extinction
182
occurrence in local population under the conditions of the potential changing of γ and p due to
183
exposure difference of chemicals.
184
VI.Estimating Annual Survivals of Roach and Mating Probability from Field Survey.
185
The annual survivals of roach can be estimated using Eqs. 5-6 in main text from the
186
abundance of different age-class. The abundance of age-class III composition was the highest
187
in all age groups of roach catch (10). Thus, annual survival rates can be estimated for two
188
sub-populations, i.e. those age classes I to III (1 to 3 years of age) and those greater than 3
189
years of age. The catch curves and the annual survivals in watersheds were regressed based on
190
the field surveys of roach catch (10, 11) as shown in Figures S4-S13. Using the Jarque-Bera
191
goodness-of-fit test (12), the probability distributions of male annual survivals of age
192
III-XVIII class groups were tested to be normality distribution (H=0, p-value=0.1925, where
193
H represents null hypothesis) with mean (0.4975) and standard deviation (SD) of 0.1414
194
(Matlab Ver.6.5). By the same way, the probability distributions of female annual survivals of
195
age III-XVIII classes were also normality distribution (H=0, p-value=0.1673) with mean of
196
0.5291 and SD of 0.1459. As the precondition of the Eqs.5-6, it was required that the slopes of
197
the catch curves should be negative (14, 15). And therefore, the data point before t=3 as
198
shown in Figures S6-12 can not be used to estimate the survival rates of age classes I-III.
199
Only the catch data of age classes I-III which were reported in the Orava valley reservoir in
200
north-west Slovakia show depressive trend as shown in Figure S-13, and annual survivals of
201
the male and female of age classes I-III were estimated to be 0.118 and 0.123, respectively.
202
Considering the individuals of age classes I-III and III-XVIII in same inhabits suffering the
S10
203
same environmental impacts, their annual survivals were assumed to have the similar
204
fluctuation ranges. Thus, the SDs of male and female in age classes I-III were estimated to be
205
0.0343 and 0.0339, respectively, based on the ratio between SD and mean of age classes
206
III-XVIII since the sensitivity of annual survivals of age class I-III to the population response
207
contributes less than 10% of the total in two-sex matrix. The all annual survivals of Roach
208
were shown in Table S1.
209
In field roach population, not all attend the spawning every year. On the other hand,
210
considering the difference of sex mature time in roach individuals, the proportion attending
211
spawning population is distinct in each age group. According to its definition, the mating
212
probability can be calculated by Eq. S-24:
213
ϕf =
nspawn,i
n
(S-24)
total ,i
214
where φf is the mating probability of female (or male); nspawn,I is the female (or male) relative
215
number of age i group in spawning population; ntotal,I is the female (or male) relative number
216
of age i group in total population. In this study, the mating probabilities of male and female
217
were estimated using the population structure of spawning fish, and the whole population
218
surveyed at Jelesna Brook in Russia (11) (Table S2).
219
VII.Uncertainty Analysis. The two-sex population model, of which elements were resampled
220
by Monte-Carlo and bootstrapping methods, were applied to estimate the population response
221
uncertainty (i.e. intrinsic population growth rate (λ), Maximum Sustainable Yield (MSY), and
222
Extinction Risk (ψ)). The sensitivity of elements to eigenvalue (λ) of two-sex matrix provided
223
a profile of uncertainty analysis (Figure S14). The fertility rates (Fi) and survival (P0,1)
224
contributed more than 90% of the variation in population growth rate. Thus, the uncertainty
S11
225
source of two-sex matrix was divided into two parts, i.e. fertilities and annual survivals. The
226
fertilities were predicted by fertilization kinetic function (Eq. 11), embedded by relations of
227
TLs-k (Eq. 17), and γ-q (Eq.23), of which the predictive errors, were carried out by
228
bootstrapping methods. Considering a sample size of 5, the model for the relations of γ-q was
229
optimized, of which the free variable number was decreased to improve its adaptability for the
230
bootstrap resampling method (Figure S2). The annual survivals were simulated by
231
Monte-Carlo method, of which distributions (Table S1) were derived from a serial dataset
232
from the field survey literatures (10, 11), which covered different kinds of roach natural
233
inhabits
234
Using the resampling methods, the MYS Loss with 400 resampling trials was carried out
235
as shown in Figure S15. Any trial indicates that roach MSY Loss changes with increment for
236
severity index of intersex under a specific situation. The deeper the color, the higher the
237
probability of situation occurrence in natural environment. When there existed the conditions
238
of intersex occurrence, we stimulated the local extinction probability (ψ) roach populations
239
caused by sex ratio bias due to selective fishing using the same way as above (400 trials)
240
(Figure S16).
241
242
243
244
245
S12
246
Reference
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
(1) Vogel, H.; Czihak, G.; Chang, P.; Wolf, W. Fertilization kinetics of sea urchin eggs. Math.
Biosci. 1982, 58, 189-216.
(2) Kiflawi, M.I. Game allocation and fertilization success in coral reef fish. II. Using
developmental instability to address questions in community and behavioral ecology.
University of New Mexico, Albuquerque, New Mexico, 1999.
(3) Calus, W. Lek-like spawning behaviour and different female mate preferences in roach
(Rutilus, rutilus). Behaviour 1996, 133, 681-695.
(4) Jobling, S.; Coey, S.; Whitmore, J.G.; Kime, D. E.; Van Look, K.J.; McAllister, B.G.;
Beresford, N.; Henshaw, A.C.; Brighty, G.; Tyler, C.R.; Sumpter, J.P. Wild intersex roach
(Rutilus rutilus) have reduced fertility. Biol. Reprod. 2002, 67(2), 515-24.
(5) Ramsey, J. Models specification error, and inference: a discussion of some problems in
econometric methodology. Oxford. B. Econ. Stat. 1970, 32(4), 301-318.
(5) Newman, M.C., Quantitative methods in aquatic ecotoxicology. CRC, Boca Raton: FL,
USA, 1995.
(6) Chernyavsky, V.I.; Kuliev, Z.M.; Aminova, I.M.; Belova, L.N. Rutilus rutilus caspicus
(Jakowlew, 1870). In http://www.caspianenvironment.org/biodb/eng/fishes/Rutilus%20
rutilus%20caspicus/main.htm: 2007.
(7) Newman, M., Regression-analysis of log-transformed data-statistical bias and its
correction. Environ. Toxicol. Chem. (SETAC) 1993, 12, 1129-1133.
(8) Jobling, S.; Williams, R.; Johnson, A.; Taylor, A.; Gross-Sorokin, M.; Nolan, M.; Tyler, C.
R.; van Aerle, R.; Santos, E.; Brighty, G. Predicted exposures to steroid estrogens in U.K.
rivers correlate with widespread sexual disruption in wild fish populations. Environ.
Health Perspect. 2006, 114 Suppl 1, 32-9.
(9) Jobling, S.; Nolan, M.; Tyler, C.R.; Brighty, G.; Sumpter, J.P. Widespread sexual
disruption in wild fish. Environ. Sci. Technol. 1998, 32(17), 2498-2506.
(10) Hartley, P.H.T. The natural history of some British freshwater fishes. Proc. Zool. Soc.
Lond. 1947, 117, 129-156.
(11) Juraj, H. Age, growth and life history of the roach Rutlius rutilus carpathorossicus
Vladykov, 1930, in the Orava valley reservoir. Zoologicke Listy 1967, 16(1), 87-97.
(12) Jarque, C.; Bera, A. A test for normality of observations and regression residuals. Int.
Stat. Rev. 1987, 55, (2), 1-10.
(14) Ricker, W.E. Computation and interpretation of biological statistics of fish populations.
Bull. Fish Res. Board Can. 1975, 191, 382.
(15) Williams, W.P. The Growth and Mortality of Four Species of Fish in the River Thames at
Reading. J. Anim. Ecol. 1967, 36 (3), 695-720.
285
286
S13
TABLE S1. Natural Life History Parameters of Wild Roach Population. Pm: survival of female; Pf: survival of male; L: length of roach. Eggs:
annual numbers of eggs produced by a female. Age class I, II…III in the first row refer to 1, 2…18 years of age. Mean and SD are the mean
value and standard deviation of normality (norm) probability distribution (Prob.Distr.). Min and Max are the minimum and maximum value of
uniform probability distribution.
Ages
Parameters
Pm
Pf
Zygote
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII XIV XV
XVI
XVII XVIII
Mean(Min)
0.022
0.118
0.498
0
SD(Max)
0.079
0.0343
0.141
0
Prob. Distri.
uniform
norm
norm
norm
Mean(Min)
0.022
0.123
0.118
0.529
0
SD(Max)
0.079
0.0339 0.0339
0.146
0
Prob. Distri.
uniform
norm Norm
norm
norm
TL (mm)
k (103)
Fi
--0
42
-0
58
-0
72
88
99 105 126 142 155 180 200 216 233 243 247 258 260 264
4.9 6.3 7.5 8.2 11.4 14.7 18.0 26.5 36.2 46.5 60.6 70.8 75.4 89.5 92.4 98.3
0
2255 2562 5703 9300 13499 19932 27223 34935 45536 53218 53 56642 67237 69366 73829
218
S14
TABLE S2. Age Structure in the Spawning Subpopulation and Whole population. The mating probability was estimated by the rate of spawning
proportion in different age group.
Age class I, II…III in the first column refer to 1, 2…18 years of age.
I
II
III
IV
V
VI
VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII
Age
Sex
Whole population
Spawning
Male
subpopulation
φm
Whole population
Spawning
Female
subpopulation
φf
214
41
11
3
1
73
57
1
1
1
1
1
1
0.6 0.705 0.781
29 125 128
12
83 108
1
5
5
1
1
1
1
0
0
1
1
1
1
1
1
0.4 0.414 0.664 0.844
1
1
1
1
1
1
0.268 0.333
331
56
5
3
2
0.054
35
21
88
62
S15
0
2
0
0
0
1
5.0
Eggs Clutch size (*103)
4.5
4.0
3.5
3.0
2.5
2.0
1.5
2.6
2.7
2.8
2.9
3.1
3
3.2
3.3
Body length (natural logarithm, units: cm)
FIGURE S1. Relation between eggs clutch size and body length of female roach. The blue
star (*) indicates the surveyed dataset of clutch size with body length size. The black line
represents the fitted curve. The red dash lines are the 95% confidence interval boundaries of
the fitted curve.
S16
Reduction of fertilization success (q)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
Intersex Severity Index (γ)
6
7
FIGURE S2. Fitting curves between reduction of fertilization success (q) of male roach and
intersex severity index (γ) using bootstrap method. The red cycle (o) indicates the surveyed
dataset from field. The blue line represents the simulated all the predicted curves using
bootstrap resampling method.
S17
1
0.8
Incidence
λ=1
0.6
0.4
0.2
0
1
2
3
4
5
6
7
Severity Index
FIGURE S3. Contour of λ=1 under different sex ratios (solid line δ=0.05) with specific
intersex index and incidence. Deeper color represents higher λ.
S18
6
5
Ln(Nt)
Ln(Nt)=-0.7704t+ 7.5791
R2 = 0.8658
Female
Male
4
3
2
Ln(Nt) = -0.9822t + 6.7314
R2 = 0.9293
1
0
0
1
2
3
4
5
6
7
t (year)
FIGURE S4. Average catch curves of roach in the Norfolk Broads in the period 1939 and line
of the equation lnNt=-Z×t+a for the III-VI age-groups. t-age, Nt-number of fishes of t age
group, a–intercept, Z-slope rate. Solid line represents male average catch curve, from which
the annual survival of older than III age groups was calculated to be 0.374 using equation
Eq.E 5); Dashed lines represents female average catch curve, and the annual survival be
0.463.
S19
5
Ln(Nt)
4
3
2
Female
Male
1
Ln(N) = -0.2909t + 5.413 R2 = 0.7379
Ln(N) = -0.7272t + 6.0396 R2 = 0.702
0
0
1
2
3
4
5
6
7
t (year)
FIGURE S5. Average catch curves of roach in the Norfolk Broads in the period 1940 and
lines of the equation lnNt=-Z×t+a for the III-VI age -groups. t-age, Nt-number of fishes of t
age group, a–intercept, Z-slope ratio. Solid line represents male average catch curve, from
which the annual survival of older than III age groups was calculated to be 0.483 using
equation Eq. 5); Dashed lines represents female average catch curve, and the annual survival
be 0.748.
S20
6
y = -0.9419x + 8.8771
R2 = 0.8824
5
Ln(Nt)
4
3
2
Female
Male
1
y = -0.6743x + 6.3699, R2 = 0.8382
0
0
1
2
3
4
5
6
7
8
9
t (year)
FIGURE S6. Average catch curves of roach in the Norfolk Broads in the period 1938-1940
and line of the equation lnNt=-Z×t+a for the III-VI age –groups. t-age, Nt-number of fishes of
t age group, a–intercept, Z-slope ratio. Solid line represents male average catch curve, from
which the annual survival of older than III age groups was calculated to be 0.51 using
equation Eq. 5; Dashed lines represents female average catch curve, and the annual survival
be 0.39.
S21
4.0
Female
Male
3.5
Ln(Nt)
3.0
y = -0.9718x + 6.7679
R2 = 0.9792
2.5
2.0
1.5
y = -0.9229x + 5.919
R2 = 0.870
1.0
0.5
0
0
1
2
3
4
5
t (year)
6
7
8
FIGURE S7. Average catch curves of roach in the Old West River of in the period 1939-1940
and lines of the equation lnNt=-Z×t+a for the III-VII age –groups. t-age, Nt-number of fishes
of t age group, a–intercept, Z-slope ratio. Solid line represents male average catch curve, from
which the annual survival of older than III age groups was calculated to be 0.397 using
equation Eq. 5);Dashed lines represents female average catch curve, and the annual survival
be 0.378.
S22
3.5
y = -0.6433x + 5.1979
R2 = 0.9565
3.0
Ln(Nt)
2.5
2.0
Female
Male
1.5
1.0
y = -0.4143x + 3.235
R2 = 0.6523
0.5
0
0
1
2
3
4
5
t (year)
6
7
8
FIGURE S8. Average catch curves of roach in Barrington of in the period 1939-1941 and
lines of the equation lnNt=-Z×t+a for the III-VIII age – groups. t-age, Nt-number of fishes of t
age group, a–intercept, Z-slope ratio. Solid line represents male average catch curve, from
which the annual survival of older than III age groups was calculated to be 0.661 using
equation Eq. 5);Dashed lines represents female average catch curve, and the annual survival
be 0.525.
S23
4.5
4.0
3.5
3.0
2.5
y = -0.6657x + 5.6724
R2 = 0.5474
Ln(Nt)
Ln(N )
Female
Male
2.0
1.5
1.0
0.5
0
y = -1.0947x + 6.6668
R2 = 0.9465
0
1
2
3
4
5
t (year)
6
7
8
FIGURE S9. Average catch curves of roach in Grantham Canal of in the period 1939 and
lines of the equation lnNt=-Z×t+a for the III-VI age –groups. t-age, Nt-number of fishes of t
age group, a–intercept, Z-slope ratio. Solid line represents male average catch curve, from
which the annual survival of older than III age groups was calculated to be 0.335 using
equation Eq. 5);Dashed lines represents female average catch curve, and the annual survival
be 0.514.
S24
4.0
3.5
Female
Male
3.0
Ln(Nt)
y = -0.8979x + 6.0926
R2 = 0.7885
2.5
2.0
1.5
1.0
y = -0.7878x + 5.6739
R2 = 0.9192
0.5
0
0
1
2
3
4
t (year)
5
6
7
8
FIGURE S10. Average catch curves of roach in River Granta of in the period 1939 and lines
of the equation lnNt=-Z×t+a for the III-VII age –groups. t-age, Nt-number of fishes of t age
group, a–intercept, Z-slope ratio. Solid line represents male average catch curve, from which
the annual survival of older than III age groups was calculated to be 0.455 using equation Eq.
5);Dashed lines represents female average catch curve, and the annual survival be 0.407.
S25
4.0
Ln(Nt) = -0.8344t + 5.5257
R2 = 0.8728
3.5
Female
Male
Ln(Nt)
3.0
2.5
2.0
1.5
1.0
Ln(Nt) = -0.9359t + 5.562
R2 = 0.8906
0.5
0
0
1
2
3
4
5
6
7
8
t (year)
FIGURE S11. Average catch curves of roach in Bridge water Cannal of in the period 1939
and lines of the equation lnNt=-Z×t+a for the III-VII age –groups. t-age, Nt-number of fishes
of t age group, a–intercept, Z-slope ratio. Solid line represents male average catch curve, from
which the annual survival of older than III age groups was calculated to be 0.392 using
equation Eq. 5; Dashed lines represents female average catch curve, and the annual survival
be 0.434.
S26
3.0
Ln(Nt) = -0.3942t + 3.8641
R2 = 0.8923
Ln(Nt)
2.5
2.0
1.5
Female
Male
1.0
Ln(Nt) = -0.2476t + 1.9309
R2 = 0.8929
0.5
0
0
1
2
3
4
5
6
t (year)
7
8
9
10
FIGURE S12. Average catch curves of roach in other localities of in the period 1938-1939
and lines of the equation lnNt=-Z×t+a for the III-VII age –groups. t-age, Nt-number of fishes
of t age group, a–intercept, Z-slope ratio. Solid line represents male average catch curve, from
which the annual survival of older than III age groups was calculated to be 0.78 using
equation Eq. 5);Dashed lines represents female average catch curve, and the annual survival
be 0.674.
S27
7
Female
Male
Ln(Nt)
6
5
Ln(Nt) = -0.2777t + 4.016
R2 = 0.4314
Ln(Nt) = -0.5316t+ 5.1163
R2 = 0.2943
4
3
2
1
0
0
2
4
6
8
10
12
t (year)
14
16
18
FIGURE S13. Average catch curves of roach in the Orava valley reservoir in north-west
Slovakia in the period 1930 and lines of the equation lnNt=-Z×t+a for the III-XVIII age
–groups. t-age, Nt-number of fishes of t age group, a–intercept, Z-slope ratio. Solid line
represents male average catch curve, from which the annual survival of older than III age
groups was calculated to be 0.588using equation Eq. 5);Dashed lines represents female
average catch curve, and the annual survival be 0.758. Thin solid line represents male average
catch curve of I-III age group (Ln(Nt)= -2.1337t+ 7.66,R2 = 0.98), from which the annual
survival was calculated to be 0.118 using equation Eq. 5);Thin dashed lines(Ln(Nt)=-2.0963t
+ 8.005,R2=0.99) represents female average catch curve, and the annual survival be 0.123.
S28
Relative Sensitivity
Age(year)
13
1112
10
89
5
3 4
2
1
67
Age(year)
FIGURE S14. Relative sensitivity of roach population growth rate (λ) to its life-cycle traits
which indicates the survival probability from age i (x-axis) to age j (y-axis).
S29
MSY Loss
Severity Index
FIGURE S15. Relation between maximum sustainable yield (MSY) Loss and intersex
severity index of roach. The blue cycles (o) are the simulation result based on all the roach
life cycle traits.
S30
ψ
δ
FIGURE S16. Relation between extinction risk (ψ) and sex ratio of roach (δ) population. The
value of δ indicates the skewing degree of sex ratio from natural status of 0.5 to 1 because of
sex selective capture in fishery. The blue cycles (o) are the simulation results based on all the
roach life cycle traits.
S31