Appendix - Springer Static Content Server10.1007... · Web viewThe dose-response relationship used for modeling reproductive failure published by Schwacke et al. (2002) related to

Online resources: Appendix

Appendix

Archives of Environmental Contamination and Toxicology

Modeling population-level consequences of PCB exposure in East Greenland polar bears

Viola Pavlova , Volker Grimm, Rune Dietz, Christian Sonne, Katrin Vorkamp, Frank F. Rigét,

Robert J. Letcher, Kim Gustavson, Jean-Pierre Desforges , Jacob Nabe-Nielsen

Corresponding author: Viola Pavlova, Aarhus University, Frederiksborgvej 399, DK-4000 Roskilde, Denmark, [email protected]


Section 1Table A1 Parameter values and references

Parameter Value Units Parameter meaning References & notesσy 0.916 - survival probability of a yearling Regehr et al. 2010

σc 0.57 - survival probability of a cub assumption as in Pavlova et al. 2014

β0 0.437 - breeding probability of female with status 0 Regehr et al. 2010β12 0.104 - breeding probability of female with status 1 or 2 Regehr et al. 2010F 6 - field metabolic energy requirement factor Pavlova et al. 2014Fy 11 - field metabolic energy requirement factor for yearlings Pavlova et al. 2014mcc 469 g/day daily consumption of milk by cub Arnould and Ramsay 1994, Derocher et al. 1993mcy 131 g/day daily consumption of milk by yearling Arnould and Ramsay 1994, Derocher et al. 1993Emc 16.9 kJ/g energy content in milk for yearling Arnould and Ramsay 1994, Derocher et al. 1993Emy 12 kJ/g energy content in milk for cub Arnould and Ramsay 1994, Derocher et al. 1993Wsm 54.5 kg asymptotic weight Pavlova et al. 2014asm 0.04247 - mass growth rate constant (seal male) Pavlova et al. 2014bsm 0.16599 - fitting constant (seal male) Pavlova et al. 2014Wsf 48.1 kg asymptotic weight of ( seal female) Pavlova et al. 2014asf 0.1114 - mass growth rate constant ( seal female) Pavlova et al. 2014bsf 0.2583 - fitting constant (seal female) Pavlova et al. 2014aTbl 0.365 - regression parameters for seal blubber calculation Pavlova et al. 2014bTbl 1.564 - regression parameters for seal blubber calculation Pavlova et al. 2014Es 37.8 (9) kJ/g (kcal/g) energy content of seal blubber Stirling and McEwan 1975FmilkC 0.275 - proportion of fat in milk in cub Derocher et al. 1993FmilkY 0.206 - proportion of fat in milk in yearling Derocher et al. 1993Ρ 0.67 - ratio of contaminant in fem. adipose tissue to milk Polischuk 1999Ac 0.23 - proportion of CB153 deposited into adipose tissue (cub) Polischuk 1999Ay 0.3 - proportion of CB153 deposited into adipose tissue (yearling) Pavlova et al. 2014A 0.1 - proportion of contaminant deposited into adipose tissue Pavlova et al. 2014μsf 0.084 - mortality of adult female bear Regehr et al. 2010μf 0.053 - mortality of subadult female bear Regehr et al. 2010


π1cub 0.276 - probability of single cub in a litter Regehr et al. 2010Ff 0.28 - fat proportion in a female bear assumption as in Pavlova et al. 2014Fpf 0.4 - fat proportion in a pregnant female bear Polischuk 1999Ffc 0.23 - fat proportion in a female bear with cubs assumption as in Pavlova et al. 2014Ffy 0.28 - fat proportion in a female bear with yearling assumption as in Pavlova et al. 2014Wpf 371 kg weight of a pregnant female Polischuk 1999Wfc 161 kg weight of a female with cubs Polischuk 1999Wbf 185 kg asymptotic weight of bear female Derocher and Wiig 2002kbf 0.58 - mass growth rate constant of bear female Derocher and Wiig 2002Abf -0.578 - fitting constant of bear female Derocher and Wiig 2002Fc 0.11 - fat proportion in a cub Polischuk 1999Fy 0.28 - fat proportion in a yearling Polischuk 1999

Wc 43.5 kg weight of a cub Polischuk 1999

Wy 90 kg weight of a yearling Polischuk 1999

has 18 % % of seals, 3-19yrs, among all seals killed by a bear/year Stirling and Øritsland 1995

hsp 56 % % of seal pups among all seals killed by a bear/ year Stirling and Øritsland 1995

ar 1.000 - coefficient – rep. failure dose-response relationship [Eq.1] Fit based on data from Schwacke et al. 2002

br 46.890 - coefficient –rep. failure dose-response relationship [Eq.1] Fit based on data from Schwacke et al. 2002

cr 0.117 - coefficient –rep. failure dose-response relationship [Eq.1] Fit based on data from Schwacke et al. 2002

ap 2.063 - coefficient-linear model sum-PCB ~ CB153 (Appendix) Based on E. Greenland data by Dietz et al. 2013

bp 1568.7 - coefficient-linear model sum-PCB ~ CB153 (Appendix) Based on E. Greenland data by Dietz et al. 2013


Section 2

Correlation of sum-PCBs and CB153

The dose-response relationship used for modeling reproductive failure published by Schwacke et al.

(2002) related to Aroclor 1254 concentrations. Because the original model by Pavlova et al. (2014) only

operated with the congener CB153, we used data on polar bear sum- PCBs concentrations from East

Greenland (from Dietz et al. 2013) to estimate the correlation of CB153 and sum-PCBs.

Because PCB congeners 87, 101_84,105, 110 , 118, 128, 138, 151, 153, 180 and 183 typically occur

in Aroclor 1254 (Draper and Koszdins 1991), we included these congeners in the sum-PCBs. The data on

adipose tissue concentrations for 103 female polar bears (sampled during 1984 - 2009) were normalized to

lipid weight.

The Pearson’s correlation coefficient between the bears’ CB153 concentrations and sum-PCB

concentrations was determined to be 0.9920166. The correlation was highly significant: t = 88.9984, df =

128, p-value < 2.2e-16 95 percent confidence interval: 0.9887142 0.9943554)

We therefore concluded that CB153 is a good predictor of sum-PCB concentrations. We further used a

linear model to quantify the relationship. The estimated coefficients of the model:

Sum-PCB = ap (CB153) + bp [A1]

were ap = 2.063 and bp = 1568.7 (Residual standard error: 1292 on 128 degrees of freedom Multiple R-

squared: 0.9841, Adjusted R-squared: 0.984 F-statistic: 7921 on 1 and 128 DF, p-value: < 2.2e-16)

This linear model was used to predict the sum-PCBs concentrations in bear adipose tissue from the

concentrations of CB153 whenever needed (see ODD, Online resources: Appendix, Section 3).

Additional reference

Draper WM, Koszdins S (1991) Speciation and Quantitation of Aroclors Based on PCB Congener Data:

Application to California Mussels and White Croaker. J. Agric. Food Chem. 39, 1457-1467 1457


Section 3

Overview, Design & Details (ODD) protocol:

Modeling population-level consequences of PCB exposure in East Greenland polar bears

This document presents a thorough documentation of the model used in the manuscript “Modeling

population-level consequences of PCB exposure in East Greenland polar bears” by Pavlova and coauthors.

The original version of the model was developed by Pavlova et al. (2014). Here we present all changes to the

original model by presenting the original ODD protocol by Pavlova et al. (2014) merged with the description

of all new processes. All lines that do not originate from Pavlova et al. 2014 (ODD, in Supporting

information) are underlined. To pinpoint the important changes, some no longer valid lines of the original

protocol were stricken through.

1.1 Model description

This model description follows a standardized protocol for describing individual and agent-based

models - the ODD (Overview, Design concepts, Details) protocol (Grimm et al. 2006, Grimm et al. 2010).

Purpose. The purpose of the original model was to produce predictions of CB153 concentrations in

adipose tissue of a whole population of polar bears in East Greenland between 1986 and 2009. The purpose

of the amended model was to predict changes in population growth rate as a result of modeled health effects

associated with PCB contamination.

Entities, state variables and scales. The only entities in the model were polar bear individuals

females, two years old or older. Females Bears were characterized by their age (2–30 years), sex, yearly

requirement of energy [kJ](equal to EFC for females with cubs, EFY for females with yearlings and EA for all

other bears), weight W [kg], pregnancy status “p” (true or false), the proportion of storage blubber “fat”,

and total body burden of CB153, BB [ng]. The reproductive status “status” was set to zero for female with no

offspring, to one for female with cubs, two for females with yearlings and five for males. In the cub mortality


scenario two supporting variables were added: temporary body burdens Temp_B B [ng] and temporary energy

requirements Temp_energy [kJ] .

Cubs and yearlings were not represented as individual agents because their contamination level was

dependent on the contamination level of their mother. Instead, the following variables of females

represented the attributes of their offspring: number of offspring,” ofno” [0, 1 or 2], body burden of a cub,

BC, body burden of a yearling, BY , energy needed by a yearling, Ey, and the number of days of survival for

each offspring (“days1” and “days2”). Siblings (the offspring born in the same litter) were assumed to have

equal milk consumption rate, energy requirement and weight and thus also their contaminant body burden

equaled. The model was not spatial and proceeded in annual time steps. We simulated the period between

1986 1925 and 2009. The only environmental variable was the content of CB153 in seals.

1.2 Process overview and scheduling

The model consisted of submodels as described below. These were processed during each time step

(year) in the order as presented in the text. In all submodels the order of processing the single agents (bears)

was randomized and variables were updated immediately. For the implementation of the submodels and

references, see section 1.6 below.

Dependent on the implemented health effect (abortion, death of a cub), the model included additional

processes as described below.

Offspring survival and pregnancy submodels. First, it was determined whether the polar bear cubs

would survive the simulated year and if not, for how many days of the year they survived. This related to

natural survival of cubs only, i.e. the PCB levels of mothers were not addressed here. Second, it was

determined whether females that were not pregnant would become pregnant during the simulated year.

Update weight and Update blubber submodels. In Update weight the weight of bears was calculated

according to a von Bertalanffy growth function or set according to reproduction status. Update blubber

served for updating the proportion of body fat of each bear according to sex and status.

Set energy requirements submodel. This procedure calculated the energy requirements of each bear

according to its reproductive status, weight and for how many days they lactated.


Feed submodel. Each bear female satisfied its annual energy requirements by feeding on seals. With

each seal consumed, the bears correspondingly females correspondingly increased their contamination

burden by the amount present in the seal blubber multiplied by deposition efficiency. All bears satisfied their

energy needs, i.e. there was no competition for resources incorporated in the model.

PCB cub mortality submodel. This submodel was employed only when modeling the scenario of

increased cub mortality. Here, females with cubs, that were selected to survive the given year, were

evaluated for their sum-PCBs concentrations and probability of cub loss. The probability of PCB-attributed

mortality of each cub was determined according to the dose-response relationship for reproductive failure

(Eq. [1], main text). Whenever a cub was selected to die, a new number of its survival days ( days1 or days2 )

was randomly determined (values between 1 – 365 days). Now the body burdens of the mother were

updated according to the newly determined number of days of lactation. Lactation transfer submodel. The

proportion of contaminants that was transferred to the milk was subtracted from the total body burden of

lactating females. The subtracted amount depended on the number of offspring, their age and the number of

days they survived. The contamination in the offspring was also updated.

Population dynamics submodel. Bears survived or died according to given survival probabilities,

irrespective of energy status or contaminant load. Females with surviving yearlings weaned them. For each

weaned yearling a new two years old individual was created. Half of the weaned offspring (that would

represent males) were removed from the model on a random basis. The mating status and pregnancy status of

females were updated.

Whenever the abortion scenario was simulated, the sum -PCBs concentrations of pregnant females

were determined from their CB153 body burdens in order to predict the possibility of a PCB-associated

abortion. According to the probability of fetal loss, which was calculated using the dose-response

relationship [Eq. 1, main text ], females either aborted their pregnancy and returned to status “single” or

proceeded to status “with cubs”.

Update age.

Update weight and Update blubber (again) submodels. (See description above).


1.3 Design concepts

Basic principles. The basic principles implemented in the original model were feeding of polar bears

on seal blubber, followed by partial deposition of the CB153 contained in consumed blubber and the

subsequent transfer of contaminant from mothers to offspring via lactation. This principle remained in the

amended version, however in the new model the main focus was on the impact of the sum-PCBs attributed

health effects on the population growth. Dependent on the sum-PCBs concentrations in adipose tissue of

females, they either failed to produce cubs or lost them during the first year of their life. Emergence. The

contamination levels in individual adult polar bears emerged from the interaction of their feeding behavior

and their reproductive activity. The population growth rate was an emergent property of the model and was

influenced by the decreased reproduction associated with PCB exposure. Stochasticity. To reflect

environmental variation, Demographic rates used were based on data collected in the period 2001–2006 from

the Southern Beaufort Sea polar bear population (Regehr et al. 2010) (with the exception of cub survival

probability, see section 1.6 Submodels for details). The exact date of offspring death was a randomized

variable and affected the female contamination level. The sex of the seals predated by each polar bear was

chosen randomly.

Observation. The concentration of CB153 was recorded yearly for individual bears. We only used the

output for the period 1986–2009 as our model results. The focal output was the growth rate, but we also

measured the trend in sum-PCBs concentrations in females dependent on age. The modeled polar bears had

no adaptive behavior, thus the design concepts adaptation, prediction, sensing, and learning as proposed in

(Grimm et al. 2006 and Grimm et al. 2010) did not apply. We also neglected any possible interactions (such

as competition, territoriality etc.) among bears with the exception of the mother – offspring contaminant

transfer and therefore the concepts interactions and collectives as in (Grimm et al. 2006 and Grimm et al.

2010) did not apply either.

1.4 Initialization

The bear population size in East Greenland is unknown, although it has been roughly estimated at

2,000 individuals [70]. We used this value as the initial population size The initial population consisted of


200 individuals in order to increase the speed of calculations. The starting year was 19251950 and

simulations were run for 85 years. The early start date for simulations was necessary to reach a stable age

structure in the population and also to allow for the accumulation of contamination in polar bears to the 1986

level.

The sex and age (2-20 years) of the bears were assigned randomly. Initial status of adult females was

set randomly as well as the number of their offspring. Weight was calculated according to von Bertalanffy

equation for polar bears (Derocher and Wiig 2002) and the fat proportion was determined using the Update

blubber submodel (see section 1.6). The initial contaminant concentration of all bears was set to 0.

1.5 Input data

Contamination of modeled polar bears was driven by seal consumption. The contamination of each

seal age class in every year of simulation was predicted by the linear model fitted to the available data on

ringed seal contamination as described in Supporting Information S3 in Pavlova et al (2014).

1.6 Submodels

For parameter symbols, definitions, default values, and sources for parameterization, see Table A1.

Offspring survival and pregnancy. The survival of the offspring and the possibility of pregnancy in

females without offspring were determined according to probabilities as in Table A1 (values mostly from

Regehr et al. 2010). Whether offspring would survive the simulated year and which females would become

pregnant was determined in order to allow accurate subsequent calculation of the energy demands of females

(we accounted for access energy needed during pregnancy and for production of maternal milk). The exact

number of days of offspring survival was equal to 365 (for a surviving offspring). Because the data by

Regehr et al. (2010) were not seasonal we assumed a uniform probability of death during the whole year.

Thus if offspring was predicted to die during the modeled year the number of days of its survival was

randomly chosen from the interval [1-365]. Whether the offspring survived and the exact number of survival

days was determined independently for each sibling. Single adult females (aged 5 years and older) and

females who would lose the offspring during the simulated year could become pregnant according to

probability β0 and β12 , respectively (Table A1). Neither survival nor breeding was connected to energy levels


or contamination. It should also be noted that the survival probability of cubs σc had to be increased to 0.57,

compared to that in Regehr et al. (2010) in order to establish a slowly growing population.

Set energy requirements. The model did not include individual energy budgets, since corresponding

data were not available. Annual energy requirement was only included as a state variable to determine the

amount of seal blubber a bear consumed within a year, which in turn determined its contamination. The

yearly energy requirement of an adult bear, EA [kJ], was calculated based on the Kleiber’s rule (Kleiber

1975) as:

EA=365 κ f A 70 W 0 .75

[A2]

where W is the mass [kg] of the bear, κ converts kilocalories to kilojoules and equals 4.2 and fA is a

parameter adjusting for the field metabolic rate, further on referred to as “field metabolic factor” in bears two

years old and older. The value of f A was set to 6 according to findings by Pavlova et al. (2014). The value of

fA is not very well known for East Greenland polar bears and therefore we tested the influence of its value on

the output.

In order to reflect higher energy needs of reproducing females, the yearly energy demand of females

with cubs, EFC [kJ], or with yearlings, EFY [kJ], was equal to EA plus the total amount of energy contained in

the milk produced by the female during the year (we neglected any additional energy expended on taking

care of offspring because of lack of data):

EFC=EA+mcc Emc∑i=1

2

daysi

[A3]

EFY=E A+mcy Emy∑i=1

2

daysi

[A4]


where daysi is the number of days each offspring survived and i the number of the first and second

offspring, Emc (Emy) is the energy content of milk for a cub (yearling) per gram [kJ/g], and mcc (mcy) the

consumption of milk by a cub (yearling) [g/day] (Arnould and Ramsay 1994, Derocher et al. 1993) (Table

A1). Because the energy demand of a growing cub was otherwise difficult to determine we assumed that in

the first year of life the daily energy need equaled the energy gained from daily milk consumption as

published by (Arnould and Ramsay 1994, Derocher et al. 1993). Thus the contamination in the bodies of

cubs originated only from milk. Because yearlings feed on seals and are also breast fed it was necessary to

estimate the burden of CB153 originating from both these sources. The amount of energy gained by seal

consumption (EYS ) [kJ/year] during a year was calculated as the difference between the yearly energy

requirement calculated in eq.[A2] (using age specific parameters for yearlings) and the energy received from

nursing as published in (Arnould and Ramsay 1994, Derocher et al. 1993):

EYS=365 (κ f Y 70 WY 0. 75−mcy Emy)

[A5]

The value of f Y was set to 11 according to findings by Pavlova et al. (2014). The ratio between the

yearling’s and mother’s annual consumption of seals, ε, was thus calculated:

ε=EYS

EFY

[A6]

According to this ratio, combined with the contribution from milk, the yearling was subsequently

assigned its PCB contamination level in the Lactation transfer submodel (eq. [A14]). During the simulations

of the cub mortality scenario, the estimated value of the variable energy was also stored as a temporary

variable Temp_energy , which was later used in the PCB cub mortality submodel.

Feed. The yearly energy requirement (EA, EFC or EFY) was satisfied by consuming ringed seals. To

simplify matters we assumed that only the blubber of the seal is consumed, as this is often the case in nature


(Smith 1980). Each bear in the model would enter a cycle of catching seals whose sex was randomly

determined and whose age was determined according to the hunting preferences of polar bears. We used

information on the percentage of seals of different age categories among all seals in the typical annual kill of

a polar bear (Stirling and Øritsland 1995) to model the hunting preference of bears. The categories were: seal

pups (0 years), 1 – 2 years old and 3 - 19 years old. The exact age of the seals within these categories was

random. The concentration of CB153 in blubber that corresponded to the age of the seal and the given year,

CSeal [ng/g] lw, was taken from a list of concentrations predicted from data as described in Pavlova et al. 2014

(values included in the program code presented in Supplementary Information in Pavlova et al. 2014). The

total amount of contaminant in the blubber of each seal, IC [ng], depended on the concentration of PCB in the

blubber, CSeal [ng/g] lw, and the total weight of its blubber Tbl [kg] (which has been calculated according to

the age of the seal using equations [S1] and [S3] in Pavlova et al. (2014)):

I C=103 T bl CSeal[A7]

For years 1950–1985 we used the 1986 contamination concentrations in ringed seals from

Ittoqqortoormiit (Scoresby Sound), because no data was available on the contamination of seals in East

Greenland prior to 1986. As a simplification we assumed that the seal blubber consisted of 100 % lipids (the

mean lipid content in blubber of ringed seals in samples from East Greenland was close to 100%, as noted in

Supplementary Information S3 p. 1 in Pavlova et al. 2014.) The energy gain G [kJ] from each seal was equal

to:

G=103 T bl E s [A8]

where Es was energy per gram of seal blubber [kJ/g].

The bear repeatedly consumed seals until it satisfied its annual energy demand. Seals were not

assumed to be a limited resource and competition for them did not occur in the model. The amount of CB153

that was finally incorporated in the adipose tissue of a polar bear depended on the value of AA, the deposition


efficiency. The value of A A was set to 0.1 according to findings by Pavlova et al. (2014). The values of

deposition efficiency AA tested were [0.1, 0.2 – 1], which corresponded to [10, 20 – 100] % of contaminant

being stored in the adipose tissue. For cubs, the deposition efficiency was set to 0.23, according to our

calculations based on literature findings (Polischuk 1999). The value of A Y was set to 0.3 according to

findings by Pavlova et al. (2014). In yearlings we tested various values of deposition efficiency AY [0.1, 0.2

– 1]. We did not model any other explicit elimination pathway.

PCB cub mortality submodel.

Females with an all-year surviving offspring were evaluated for their sum-PCBs concentrations and

the associated probability of offspring loss. For this purpose sum-PCBs concentrations in females were

calculated from the CB153 concentrations using relationship [A1]. The sum-PCBs concentrations

represented a mean value that the female would exhibit during the simulated year if she did nurse her cubs

for the duration of the whole year. A no-adverse effect level (NOAEL) was set to 1825 ng/g lw (the value

determined as the critical concentration for reproductive effects of Aroclor 1260 on polar bears by Sonne et

al. 2009). If a female exhibited a higher sum-PCBs concentration than this NOAEL, the probability of the

loss of a cub was calculated using [Eq. 1, main text]. If the cub was selected not to survive the given year,

the days of its survival were updated to be between 1 - 365 days (random uniform distribution).The value of

the female’s ofno variable (number of cubs) was reduced by the number of cubs that would not survive. The

female’s CB153 body burdens were then updated. First, the female’s energy requirement was recalculated

using equations [A2 and A3] and using the newly determined numbers of lactation days. Second, the ratio

between the original (stored as variable Temp_energy in submodel Set energy requirements ) and the newly

determined energy requirements was calculated. The increment of CB153 contamination from all seals

consumed during the given year was multiplied by this ratio. Finally the original female’s CB153 body

burdens (stored in the variable Temp_B B) were increased (prior entering the Feed submodel ) by the

recalculated amount of contaminant.

Lactation transfer submodel. The body burdens of females with offspring decreased during the

lactation period. The offspring on the other hand consumed an equivalent amount of contaminant from the

mother and accumulated it partially in their adipose tissue. We assumed that the amount of the transferred


contaminant, M, was dependent on the concentration of CB153 in the blubber of females. However because

the time step of our simulation is one year and the mothers of cubs undergo a massive change in weight and

fatness during that period, we used an average weight calculated from the weight of pregnant females Wpf

and weight of females with cubs Wfc (Table A1) and also averaged the fat content of the two (Ffc in female

with cubs and Fpf in pregnant female, Table A1) to calculate the average concentration of CB153 in the

adipose tissue of a female with cubs:

C fc=BB

103 (W fc+W pf

2 )(F fc+F pf

2 )

[A9]

Subsequently the body burdens BB of the mother decreases by the amount of contaminants transferred

via the milk, Mc [ng], during the year:

M c=C fc mcc Fmilkc ρ∑i=1

2

daysi

[A10]

where mcc is the daily consumption of milk by a cub [g/day] and Fmilkc is the proportion of fat in milk

for the cubs (Table A1). Parameter ρ was the ratio of contaminant concentrations in milk fat/ female adipose

tissue as calculated using data published in (Polischuk 1999) for sum-PCBs.

Contamination transfer My for females with yearlings, was determined accordingly. Female weight W

was calculated using equation [A15] described below (submodel Update weight) and the contamination

concentration Cfy [ng/g] lw for a female with yearlings was calculated as follows:

C fy=BB

103 WF fy

[A11]

The CB153 body burdens of a female with offspring were decreased by this amount (My,[ng]) of

transferred contaminant in milk during a year:


M y=C fy mcy Fmilky ρ∑i=1

2

daysi

[A12]

where mcy was the daily consumption of milk by a yearling [g/day] and Fmilky was the proportion of fat

in milk for a yearling (Table A1).

The body burden of cubs BC [ng] was determined for cubs that survived the simulated year as:

BC=365 C fc mcc Fmilkc ρ Ac[A13]

where Ac was the deposition efficiency of CB153 into the adipose tissue of a cub.

Because yearlings received contamination through both milk and seal blubber, their body burden BY

[ng] was calculated as:

BY =A y (365 C fy mcy Fmilky ρ +ε ∑1

n

( IC )n )

[A14]

where Ay is the deposition efficiency of CB153 into the adipose tissue of a yearling and ε was the ratio

of energy covered by seal consumption in a yearling to yearly energy requirement of its mother; Ic is the

amount of CB153 in each seal hunted by the mother and n the number of seals consumed by the mother and

its yearling.

Population dynamics. In the first step the bears that were to die during the simulated year were

selected according to individual death probabilities (Table A1). The maximum age was 28 30 years. In the

next step females with a surviving yearling or two weaned them and changed status to “without offspring”.

For each weaned offspring a new two years old individual with corresponding body burdens was created.

Females that weaned offspring would not become pregnant during the same year because in nature they

would be accompanied by offspring for about half a year longer. We assumed that the energy and

contamination contribution from breast feeding were negligible during the third year of life and thus the cubs


were modeled as independent agents from two years and onwards. Finally, the status of other females was

updated: females with surviving cubs changed status to “with yearlings” and pregnant females changed

status to “with cubs” (they were assigned either one cub with the probability π1cub or two cubs with

probability 1- π1cub (Table A1) .

When simulating the increased abortion rate scenario following steps were performed to select females

that would experience abortion. Firstly, sum-PCBs concentration were estimated from CB153 concentration

using relationship [A1] in females that have recently updated their status to “with cubs”. The females

retained the same weight and fat content as when pregnant. A NOAEL was set to 1825 ng/g lw (Sonne et al.

2009). Secondly, if a female exhibited a higher sum-PCBs concentration than the described NOAEL, the

probability of the loss of her fetuses was calculated using [Eq. 1, main text]. In case of fetal loss all expected

offspring would be immediately lost and her status was re-updated to “single”.

Update age. The age of all bears was incremented.

Update blubber. The proportion of polar bear fat was updated according to the values in Table A1.

Update weight. This procedure calculated weight according to von Bertalanffy growth function used

for polar bears previously (Derocher and Wiig 2002):

W =W bi (1−e−k bi(age−Abi ))3

[A15]

where W is the mass [kg] at age age, Wbi is the asymptotic weight, kbi is the mass growth rate

constant, Abi is the fitting constant (years) and i equaled f (females) or m (males) (Table A1). The weight of

pregnant females and females with cubs was also adjusted. Because no information was available to us on

the relationship between age and pregnancy weight and age and weight after nursing we used two average

values Wfc and Wpf (Polischuk 1999) (Table A1).


File output . The requested output depended on the type of simulation performed. It included

population growth rate and/or female age and sum-PCBs concentrations ( for this purpose sum-PCBs

concentrations were estimated from CB153 concentrations using relationship [A1]).

Additional references

Regehr EV, Hunter CM, Caswell H, SC, Stirling I (2010) Survival and breeding of polar bears in the

southern Beaufort Sea in relation to sea ice. Journal of Animal Ecology 79(1): 117-127.

Arnould JPY, Ramsay MA (1994) Milk production and milk consumption in polar bears during the ice-free

period in western Hudson Bay. Canadian Journal of Zoology 72: 1365-1370.

Derocher AE, Dennis Andriashek A, Arnould JPY (1993) Aspects of milk composition and lactation in polar

bears. Canadian Journal of Zoology 71: 561-567.

Stirling I, Øritsland NA (1995) Relationships between estimates of ringed seal (Phoca hispida) and polar

bear (Ursus maritimus) populations in the Canadian Arctic. Canadian Journal of Fisheries Aquatic

Science 52: 2594-2612.

Documents

Appendix - Springer Static Content Server10.1007... · Web viewThe dose-response relationship used for modeling reproductive failure published by Schwacke et al. (2002) related to